How to explain to person I'm making website for that she's responsible for hosting and domain costs etc?

I got my start as a developer this exact same way, over a decade ago. As a freelancer, part of what you are learning is to be a professional. Keep in mind, your clients are likely not tech-savvy, or they'd do this for themselves. You are the one who knows the business. Or, if you don't know it, you need to learn it. Do the research, and find out who the best hosts are, and what the costs are, that's part of your job. And if your client ends up going with an overpriced host, because you didn't help her make a good decision, that's on you.

You'll need to distinguish between jobs and favors. You might do a job at a discount, or even free, because you're new, but treat it professionally. Detail all the costs up front (yours, and third-party), and make it clear exactly what you are going to do, and what you are not going to do, how much input you're going to allow, and how many revisions, and what your overall timeframe will be. It might end up that, even free, your services aren't worth it for your friend. Why should she pay monthly fees for a website she barely uses, made by an amateur? You need to give her whatever information she needs to make an informed decision.

I try not to let this get around, but I do have a very short list of close friends and family I've done webwork for as a true favor. When I do it that way, I usually just handle everything, and bundle it under my own personal hosting account. It's just easier that way. And I don't do that for people who have a lot of demands or expectations.

I have been caught in this trap before. The best thing to do is use it as a learning experience for not offering free websites to friends if you don't have the time (really, never is my honest advice). You want to be helpful, you know how to do it, but it is never a good idea in my experience. It is always more work and drama than it is worth.

First, decide whether or not you really do want to go down this road. From what I can infer from your post, if you're already annoyed with these issues, just end this now. This is going to be a long, arduous process filled with questions and countless revisions and it's probably going to drive you nuts. For many people in the tech world, dealing with users who know nothing at all about what they are asking us to do is the hardest part of the job. It's probably also why it pays so well :-) The work is complex and it is very difficult to break it down for non-technical people. All of this takes time, time, time.

If you decide not to move forward, help with those questions about hosts and refer her to places like wix or squrespace where she can get help when needed but then can set it on auto-pilot. One session of education into the world of websites is all it will take.

If you decide you're going to do this, you may as well be prepared to field all kinds of questions, do a bunch of extra work, have them come back tons of times with revisions and additions, and then have an even more difficult time ending the "maintenance" phase, especially if you use custom code to write it that another person cannot easily pick up and do.

I know this answer is maybe not the direction you'd have expected, but from personal experience, as I mentioned, this is going to be a MUCH bigger time commitment than you expect. Build websites yourself as tests for a portfolio based on your interests. Take your time and make them look great. Don't put this added pressure of customer service. It won't help either of you in the long run. Good luck!

Edit to add: Your question of how to bill for a site creation is probably not suited for this forum. It’s complicated and done case by case. This answer is more trying to help you get out of doing things free to build a portfolio, which you can just build yourself without the added pressures involved.

It seems this person is not really tech-savy. The best thing for you to do is to come up with several hosting solutions, and summarize it to that person.

By doing so, you give knowledge. With that knowledge, the person will be able to make a choice that correspond to her needs.

There is no need to search for a complete list of solution. Like you mention, there will likely be a cheaper option that you didn't find out. The goal is to show the different categories.

Just come with 3 or 4 solutions, as diverse as you can.

There is free options (http://repl.it, github pages if the website is static, etc...), so mention it and compare it with the others.

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Of course I don't want to do any work until hosting is finalized

This is not true. If you have a contract with that person, I hope you mention in the contract that you provide only the website, not the hosting.

With a contract, it's completely fine to start working on the website even if hosting is not finalized. You should receive payment for the website anyway, not the hosting.