I remember once catching 32 magikarp and giving them all the stupidest names ever, I can't remember most of them now but I could only imagine the faces of the people who received them....
to be honest I might be one of the few people who actually got really happy when I got a magikarp on wondertrade, it was level one 1 too, I still have it but as a gyarados now
I would basically breed starter pokemon and send them to other trainers. The only time I send off zigzagoons and other early game pokemon is when other people do it to me. (which happens quite often in wonder trades)
I'm working to Masuda/IV breed a 5iv French hawlucha holding a destiny knot with a 6iv adamant hawlucha holding an everstone so I wind up with a ton of 4-6iv adamant hawluchas. I don't even consider the 4iv ones good enough to wondertrade, I release them and wondertrade the 5iv ones just because I have way too many hawluchas and will continue to get more until I get a shiny one so I figure I might as well stick with the better option. I also attach somewhat rare berries to any pokemon I send out, typically maranga and kee berries but when I run low I pick other random things like nuggets, fossils, or evolution stones.
I check IVs for everything that comes in from wondertrade too. You'd be surprised by how many 5iv pokemon I have that came from wondertrade, I seriously recommend checking everything if you can because a 5iv raltz from Japan is one of my favorite pokemon received from wondertrade.