Yes, you can do heroics. I'd suggest starting out running only with guildies; they tend to be more forgiving, and you don't run into the problem of T6 pug DPS who think you are shit because you can't tank the whole place in two pulls. (This aggravates the hell out of me, YMMV.) You can find a number of articles on what heroics are good to start with- I'm a fan of Bot, but it's not for everyone. I think anything that you like on normal is probably a good bet- being familiar with the instance is a big bonus.
As far as gear- you're looking for upgrades in both stam and defense stats at this point. I'd suggest getting some Bracers of the Green Fortress, although that may be an issue for you with the lack of gold you mentioned. Try socketing for stam more than socket bonuses, and let the avoidance come from your gear. (This is something not everyone agrees with, but it's obviously your call.) The boots from the mana tombs escort quest are awesome for avoidance, the boots from the first boss in Bot are awesome for stam. Check those out. The revered-with-Ogri'la shield or exalted-with-Sha'tar shields are both very good, try getting one of those. Run Mech and Bot (on normal) and get the Arc key; the belt reward from that quest is very nice.
Scattershot gear advice ends here, have fun, good luck.
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