Every Joel said is excellent and will add a few more things from my experience:
• When I bought or sold in GunBroker in the past I preferred USPS MO's.
• If a personal check or other payment method wait for it to clear your bank. I don't know about any specific time like 3 days or whatever, just check your bank account online or at an ATM daily. DO NOT SHIP till it clears. If your buyer is antsy over the wait, tough to be them (but tell them kindly).
• If you ship FedEx you can arrange for them to pick up from your door step, though I'd want to be there is in person to hand it to the FedEx guy. UPS you must go to their hub, which might be far away from you (and you have to declare it as a firearm I think to the clerk which may feel awkward in this state, unlike FedEx).
• Joel's offer of shipping it for you is a good one and I'd take him up on that. Delta Arsenal in Wallingford will ship a gun for you for a similar price. Greyson Guns in Orange will also, but their transfer/processing fee (in addition to shipping) is higher for non-members than Delta. You're favorite local FFL might have a similar shipping offer/fees.
• I like having a DPS3 saying the gun left my hands so I always shipped through an FFL.