Hi there @Johnsy and welcome to the forum.
Some excellent advice here from the estimable Mr. @ezbass.
The few thoughts I could add are based on my ownership of an '84 335 dot. It is indeed a fantastic and very versatile instrument, well suited to the sort of music you plan to make (not to mention Jazz - may not be your thing of course but just so I've said it...).
I've always thought it a very well balanced guitar as it happens, but that's just me I suspect. I can understand why some would consider it a touch bulky, but I've not found that to be the case personally. That said, the 339 is in most respects very similar to the 335, and the smaller body shape should address the concerns of anyone who likes the instrument but is worried about the 335's size. I tried out a 339 in a shop some years ago and liked it very much (but I still wouldn't swap my 335 for it ).
As to amps, suffice it to say there's lots out there, and choosing one needn't be a difficult task provided you're reasonably clear what sort of music you're planning to play (and I would concur with ez in that while you don't actually need an amp to make an audible noise - especially with a 335/339 style guitar - a decent amp is as much a part of the sound you make as the guitar itself). Personally I wouln't bother too much about effects at this stage, but again that's just me. IME lots of effects can become a bit of a rabbit hole if you're not careful. If the amp has them then fine, but I'd be inclined to work at getting a decent basic sound out of it to start with and think about how you can tinker with it further down the line.
As always, just my opinion.