Is it possible to get less stuff to pickup but maybe higher quality to compensate? It seems like I'm spending most of my time managing my inventory and deciding what to keep or sell. Sending a pet to town helps a bit but only a bit.

After a while I only pick up stuff that is "special" or "socketed" which would put Torchlight with every other crawler I've ever played. As someone who has played it through several times I assure you that you won't be punished for leaving boots and swords laying around.
Also you might consider investing in a Town Portal Spell, learning it, and making a quick key for it. The mana it takes is next to nothing and even without inventory problems you are going to be making A LOT of trips to town later in the game and that makes it easier to bounce back and forth.

Thank you! I worry that if I leave stuff I'll be missing out on loads of money? Enchanting stuff is expensive after all.

That's exactly what the pet is for-especially if you're grinding easier levels for XP then not having the pet is barely an issue at all.