These are the supported base sizes in 40K
Standard Infantry - 25mm round
Large Infantry - 40mm round
Monsters - 60mm round
Flyer - 90x120mm oval
Bike Bases - 25x70mm oval
Clear flight stands small - 30mm round
Clear flight stands large - 60mm round
Standard Infantry - 20mm square
Large Infantry - 25mm square
Monsters - 40mm square
Cavalry - ...
There's no hard and fast rule for it. I would suggest using a base size most appropriate for the size of the model. So if the model is Terminator sized, use a 40mm, if Dreadnought sized, use a 60mm. So convert your model and use what makes sense.
This requires a bit of good judgement and common sense. If you made a reasonable selection most people ...
It's a grey area, but it's preferred that models be played with the bases provided with them with some exceptions for scenic bases. Generally as long as you haven't modeled for a clear advantage(such as using a base that's 9" tall) most players will be OK with it. To be on the safe side, you should have a standard based guy to swap in for the scenic base ...