I suppose it could depend on what your startup actually does, but on a scale from 0 to 10 in importance I'd rate availability of a Twitter handle at a solid 0 for the vast majority of startups.
Try GetName, NameHQ, OfficialName, RealName, or some other short word that associates with your company. If you're a bakery named "Flour" in NYC, for example, then try FlourBakery, FlourBread, FlourNYC, etc. Avoid geographic terms if you're a web startup though. Once you get some traction and have legal incorporation documents, contact Twitter. If the handle isn't actively being used by a company, they'll usually give it to you. It'll take a couple months though.<p><i>Source: your friendly neighborhood naming expert. I know of a couple companies that went through this exact process. Let me know if you have any other questions.</i>