you can OC fine with a stock cooler, as long as the temps remain fine. aftermarket coolers can only help with cooler, so if your temps are fine with the stock cooler its pointless to get an aftermarket one.
to get up to 3.4ghz you'll probably need to bump the voltage up a little bit, which should be fine for the stock cooler if its a small bump. the max voltage is 1.425v which im running my phenom ii x2 550 at that 24/7 with cores unlocked sitting at 3.5 ghz and i cap out load wise bout 62c when running prime95 which is plenty fine. the max temperature for your cpu is also 74c. so with prime95 if you don't touch 70c you're fine and no you don't need more cooling, and your OC will be fine.
as a test, bump the voltage to 1.425 and run it at 3ghz to see what the temps hit. it all depends on ambient temp and general case cooling too. have a few fans in your case if you can and really clean up the wire management will make a big differences.
if it has an idle temp of 50c or something, don't even temp to load test it, just bump the volts down to maybe 1.125 first and see how high of an OC you can get with it. if you want to go higher or think the temps are safe to bump more voltage you could get 1.25 probably fine. with that mobo i believe you can set your temps manually, so it should be no problem to do so.
just mess with the multiplier too, don't do any fsb clocking if its your first time OCing and you're not really experienced with it