As with so many things in life, the answer to this questions depends entirely on how you do it.
I'd break this question down into two parts - the getting here, and the living here.
In terms of getting here, some people will satisfy the investment requirements for, and then apply for, a so-called "Golden Visa". This type of visa involves a filing fee of 5,000 Euros per person (not per family, mind you, per person), and must be renewed annually. Legal expenses in connection with this application can be in the same range as the actual filing expense itself.
This is not the best way to get to Portugal. Instead, we applied for a "pensioner's" visa (even though we did not and do not have a pension). We were able to show sufficient liquid assets to last us up to 4 months, we paid a few hundred dollars to our local Portuguese consulate, and within a month, we had our visas.
These visas entitled us to enter Portugal and remain there for four months. Four months was how long it was expected to take for us to apply for full-time resident status (which can only be done once you arrive in Portugal). We paid slightly over 350 Euros for a family of three to obtain our one-year "titulos" of Portuguese residency. We recently renewed our titulos, this time for a two-year period. That renewal cost us the same amount - 350 Euros. The fee is lower if you are from an EU country, but we were coming from the United States.
With this type of residency, no visa renewals are required. Our pensioner visa was a one and done thing. We were able to obtain our residency titulos by showing we had at least 2,000 Euros in a Portuguese bank. Financial eligibility for residency is quite easy.
We used an attorney to guide us through the entire process for obtaining our titulos. This cost us 700 Euros (and hiring an attorney for this was worth every cent).
We paid an attorney to obtain our fiscal IDs (frequently called "NIFs" or "contribuints"). This fiscal ID is equivalent to a social security number in the USA, and is indispensable to do virtually anything in Portugal. We could have filed for these ourselves online at the Portuguese tax authority's home page, easily, instantly, and for free. This expense turns out to have been unnecessary, but we didn't know better and learned that the hard way.
Portugal allows new residents to reside here for up to ten years free of Portuguese income tax on non-Portugal source income. This is called "Non habitual resident" status - which is a misleading name. Infact, to be a "non habitual resident" of Portugal, you MUST reside here full time and claim it as your tax home.
This is effectively tax-exempt status, and is a tremendous boon to foreign investors who move to Portugal. In our case, we still pay US income taxes, but US taxes on investment income are quite low compared to any European country (including Portugal, if you fall outside the non-habitual resident tax scheme). To obtain this non-habitual tax status, you must file an application. We paid an accountant 500 Euros to prepare and file this on our behalf. That was a waste of money. We could have (and ultimately did) file for our non-habitual tax status online at the Portuguese tax authority's home page. We received confirmation of our status as non-habitual residents in about two days. It took less than two minutes once I knew where to look on their web page.
In our case, it cost something on the order of 2,400 Euros to immigrate to Portugal, once you throw in the cost for things like FBI reports, (which you need in order to apply for a visa or full time residency), filing fees and legal advice. Had we handled the fiscal ID application and the online application for tax-exempt status, we would have spent 1,500 or 1,600 Euros to get here. I have friends here who have paid upwards of 30,000 Euros to immigrate to Portugal, using the golden visa application, and hiring lawyers and attorneys who, in some cases, charge absurd fees for work that only takes a few minutes to do.
The second part of the question is, how much does it cost once you are here?
Obviously, that all depends on how you live. I don't think I'm necessarily a representative case, but for what it's worth, the numbers work out like this.
We live in a beautiful compound that overlooks the city of Lisbon. Our average monthly property tax and condo fees come out to about $250 a month.
Our mobile phones, landline and unlimited internet access costs 130 Euros a month.
We now have the most comprehensive health insurance available on the market for our family. It covers everything (including things like therapeutic massage, which we don't use). We pay 250 Euros a month for that.
Our water bill is 10 Euros a month, on average.
Our electrical bill is high - about 230 Euros a month. This is because we upgraded to a commercial level electrical plan (on the normal residential plan, our lights would go out if we ran a dishwasher and toaster at the same time).
We pay 150 euros a month for our gym memberships, and 120 euros a month for private language classes.
We bought a car a few months ago. It's a BMW 1 series (slightly used, it had 1,500 kilometers on it when we bought it for 20,000 euros. We pay 310 a month for that, including our insurance, roadside assistance plan and associated costs.
We eat out very frequently. When we do, we typically spend about 30 or 40 euros for a family at a really nice restaurant. For a very expensive meal, we might spend 120 euros for a family. I typically down copious cups of coffee throughout the day. It costs .70 for an espresso.
Our largest expense by far is private school for our kid, which costs 1,300 euros a month - including door to door bus service and one-on-one tutoring each day.
There are other costs of course, but this summary gives you a flavor of about what it costs to live a luxurious lifestyle in Lisbon. On average for the last year and a half, we've spent nearly 4,100 euros a month in total - not including travel expenses, which I account for separately. What I'm reporting here are just the core, day to day living expenses you could find here if you wanted to live a very comfortable lifestyle. I am friends with several couples who live here and who are very comfortable, and they claim to spend half of what we spend (granted, they don't have kids).
One big surprise was how much it costs to buy things like a vacuum cleaner. A stand to dry wet clothes on? Eighty Euros. More or less anything imported here is going to cost a lot, and to top if off, you have a 20% sales tax. Fortunately, most people don't need more than one ironing board. We don't.
Lisbon is certainly not the cheapest part of Portugal to live in. If you live outside of Lisbon, it is possible to buy a house in a small town for 80,000 Euros and face living expenses that are roughly half of what the living expenses of Lisbon are. The reason for this is because Lisbon is basically the New York City or San Francisco of Portugal, in terms of what things cost here compared to what the same things would cost in other cities in Portugal.
The biggest cost, the cost that is in the back of your mind and that may prevent you from coming here... opportunity costs. You will not find a job in Lisbon. In fact, the terms of your visa will probably prevent it. If you do find a job, you will be paid a fraction of what you earn now. An average annual paycheck for a professional (like a teacher) is 12,000 Euros. Minimum wage is 6,000 Euros a year. The single cheapest resource in Portugal today is human capital. I hired an expert in tiles to do a month's worth of intense labor on a renovation project. Labor cost was slightly over $1,500. The same job in the USA would have cost 30 times that amount in labor (assuming you could find an expert - Portugal's tile industry is the oldest and best on Earth).
So, if your plan is to earn money here, you will have no choice but to work for yourself - in which case the opportunity cost is no cost whatsoever. For an entrepreneur, the "opportunity cost" translates directly into a massive business subsidy. Office space is cheap or, if you're savvy about it, free (Lisbon has many programs to attract new start-ups to the city, and will give out free space to qualifying businesses). Hiring qualified workers is cheaper here than anywhere else in Europe, and there is remarkably little in the way of government red tape. For my part, I run my own personal investment fund, and my office is a laptop that I carry around with me to cafes and open air markets. Doing business based out of Lisbon for someone in a similar line of work is cheap as it gets: about $1.40 worth of coffee at whatever cafe you elect to use as your base of operations. More than any other cost, opportunity cost is entirely dependent on your approach.