Number of sprockets on rear will tell you which width. Chains come in 6,7,8 (3/32"), 9 speed, 10 speed, 11 speed, I think 11 speed fits 12. Look at modernbike.com (IA) or thebikeshopstore.com (NY) stock list.
Yes you should count links. The narrow one plus the wide one is one link. Use a bread tie to mark origin.
KMC & Connex both get respect on here, FSA & camagnolo are premium for racers. sunlite & sunrace are second rate. Schwinn is low grade. There is ebike specific chain, but one user reported his didn't get any longer life than the regular kind.
Buy extra master links, the part tends to shoot off into space. The snap ones would work better with a special tool, but I used a snap ring expand tool.