First i recommend you to take away evrything that can slow down your connection adn computer, no internet clients (firefox,chrome,internet explorer,opera,netscape) it seems like no but they are actually darining computer and network resources.
Close any comunication program ( raidcall,teamspeak,messenger,skype) the last ones from my list are pretty network heavy
try to improve your machine performance, clean with the diskmanager your disk do a defrag and try to configure your computer for a smoother connection ( it is possible) with all those things i could lower my ping from constant 250 to 150, it varies from person to person but this is a improvement.
For recomended champions, well many of the old supports dont have skillshots, adc have a few for the early game or to escape, and well many bruisers like, garen,wukong,darius, skarner,..
for mages you have leblanc, akali,morde
hope those tricks and tips help you