If you are just starting out & don't want to spend the money on a tri-specific top, wear what is comfortable. Figure out whether the running or cycling top is easier to get on when you are wet, and wear that.
I second the race belt option. You can make one VERY cheap (piece of elastic & plastic clip from any fabric store). Then you don't have to worry about jackets or weather, the race belt just goes over whatever you decide to wear. Lots of the races around here have actually gotten away from race bibs - they just do the body marking now.