You might get a lot of different opinions on brands of jigs so here's some general information on some of the different types. A lot of them come in different varieties - you can find finesse football and stand up jigs etc.
Grass - rounder or more pointed head to go through grass and weeds better.
Football - Football head which is better to drag through rocks
Flipping Jigs - Bulkier, heavier gauge hook for flipping heavy cover.
Stand up - Flat bottom and will stand straight up on the bottom.
Arkie - Sort of a combination between grass and stand up.
Finesse - Usually a thinner skirt and thinner hook with shorter shank.
Swim - Cast and retrieve sort of like a spinnerbait.
Trailers -
There are bulky trailers and there are more finesse style trailers. You ca use almost anything but one of the most popular is a craw type bait like a Berkley Chigger Craw. Just keep in mind that some "flap" a lot and some don't create as much commotion on the fall. This can impact how fast a jig falls. A Berkley Chigger Craw will fall slower than a "Beaver" style bait for example.