Throw yourself in a squad as an Engineer or Medic. Your points will go up quite a bit, especially if you have a level 5 heal/repair tool.
As a career medic, I can attest that medic rakes in the points. Squad up and get your tool up and the certs will start piling up, especially during prime time.
Heavy Assault Nano 5/Resist 5 Anchor or Claw/Bruiser or Blitz Shirike/Decimator Medikit 4/4 or C-4 Hunt armor/sunderers.
everything i do as an engineer nets me constant points driving vehicles (as engie so can repair) repairing vehicles repairing turrets repairing gens laying ammo laying infantry mines laying vehicles mines on sundys them shooting them (pretty useless as proper AV mines now cause of size) planting C4 on vehicles shooting tanks with my turret shooting people with my guns
As far as an infantry class, it's no doubt engineer. Max level your ammo pack and find a big fight and just rake in the points.
ESFs, bar none. Most of the game's air hogs have an incredibly high SPM, just because it's stupidly easy to do when almost everything you destroy gives you loads of XP.
Across all characters/servers, MAXes pull in the highest score/hr. This factors everyone from the worst to the best so, barring "Are you a skygod?" type skill levels, MAX seems the way to go. As far as setup? You'll get the best score by being versatile. CQ, long range, infantry, vehicle. Know what you're up against and kit accordingly. For me, not including boosts, my HA and MAX are tied at a bit over 15k/hr. Score rankings: Max > Med > Engi > HA > LA > Infil
flying esf seemed the most reliable way to get cert for me. as starter i do suggest going on medic but you will be exposed to lots of direct fire as well.
Play as the only medic in a medium sized fight with full squad present while defending (this would be the ideal cert grind situation for me) Fly ESF with rocketpods on a low-pop continent with uncontested airspace. Play AI max with dedicated engineer/medic support in a medium sizes fight. Play uncontested babysitter for your squad max(es) as engineer in a medium sized fight.