Can I look at that source code for ideas for how I would code my web application?
Yes, of course you can! Ideas are not restricted by copyright, so everything else in your question is irrelevant.
But there are a few issues that you should consider, discussed below.
As Bart van Ingen Schenau discussed, it is easy to cross the line into copying actual code. In fact, this process should be carried out by two independent teams: one reviews the existing code and records ideas (or specifications) in a general form, and another team writes new code based on this record.
The platform is irrelevant here.
Some of the basic functionality I need
How basic is it? If other people reviewed the GPL-licenced applications, might they conclude that your paid version does not add value?
Customers would not have access to the code, so I wouldn't be distributing it or selling it.
If this was really true, then the GPL would protect you, even if you were actually copying code.
But is it true? Web applications normally have both server-side and client-side code. You need to make sure the client-side code – which you are distributing – is not “tainted” by the issues discussed above.
For the sake of completeness, note that all of this analysis would apply to most other free licences as well, including GPL3, but not AGPL3.