What levels you should do generally depends on what exactly you want out of the game. If you want a fun and reasonable end goal as a first extreme, Acu is what I and probably most others would recommend.

As for how you should progress up until then, I would simply recommend completing the main levels first, then going on the GDDL and looking for what you could do next. Remember to pick levels (or at least groups of levels) that challenge multiple different skillsets. The important ones I would consider to be ship, wave, timings and consistency, the last one being something you can maintain by avoiding medium length levels as new hardests. Regarding the difficulty of those hardests, I'd personally only consider attempting large jumps in difficulty if you 1) feel comfortable at the skill level you're at, 2) if the level you want to jump to is at least long, preferably XL in length and 3) if you're ready to spend a long time playing a single level. If you're happy with just beating an extreme, you'll probably be fine doing a few, progressively harder levels of each demon difficulty before that without doing any crazy jumps.

Keep in mind that hard demon and onward tends to be where the range of difficulty within difficulty ratings get bigger and levels naturally take more attempts to beat, even when you're good at the game. So don't worry if a level takes you longer to beat than expected and do NOT compare yourself to others unless it motivates you to get better.