Generally, third person is best for use in collaborative stories and most GMs will assume you will be writing this way. It keeps people from forgetting halfway through a post who exactly they're reading about. First person can certainly work, especially if everyone is using it and there aren't so many people that you would get easily confused (1x1s are probably the best place to use the first person). A little bit of proofreading will probably alleviate most unintentional tense switches.

On a semi-related note, I have seen people in the past who actually refuse to write in anything other than the first person (and wouldn't take no for an answer). They always struck me as the type that wanted the RP to revolve around themselves. That was just my perception though, it wasn't necessarily the case.