fizzbuzz
Which Web editors(at no charge or with costs)
is good enough to build a website
Well, you don't really need a 'web editor'. There's a straightforward process you may follow to build a website. It'd look like this:-
1. Decide on what your website will do. List out all the major features.
2. You will then need to find out which programming language is most suitable for your website. These days, you should be able build pretty much everything a sophisticated website has with PHP or Ruby.
3. Sign-In, Login, forum, chat are all 'solved' problems. Do not waste your time solving those problems again. Instead, look for integration: You can create a basic website using a CMS which will have everything - login, session handling, cookies, ability to create pages, building clean URLs and you will also have the ability to add plug-ins that will bring added functionality of chat rooms, forums etc. If you want to start - start with WordPress. You can download it from wordpress.org and get started. It's open sourced so you can modify it infinitely according to your needs.
4. If you want sophisticated forums - look for the ones in open source domain. phpBB is a great forum software that powers several large websites.
I hope this gets you started. If you have further questions, feel free to ask.