How much PoE is actually open to custom builds?

If you want to play as casually as you imply, you can use any skill. Putting your main skill gem in a 5 link, supporting it properly, and having a good skill tree will let you take almost anything through tier 6/7 maps. Beyond that, you may need to get more and more 'meta' depending on what you chose to do in the first place.

If you play how ever you want... you're going to hit progress blocks, unless you're really good at strategy. Most every character will make it through normal difficulty once you learn how to play and get the patterns down. Cruel wont be easy for a crappy build with random self-found items, but it's beatable. Merciless actually ends up being far easier than Cruel. There, acts 1-3 will get you to maps and you don't have any progress blocks in the way. Maps will overlevel you for the remaining content. Even self-found, Merciless is going to be easier than Cruel was.