No such thing as a 'church' tone my friend. If however, you're talking about sounds usually associated with worship music, then a good, clean amp will get you 80% there. Amps like the Vox AC15/AC30 or Fender Deluxe/Twin Reverb(most blackface amps actually) are commonly favoured for such applications.
Regarding your LP-related question though, the Studio or Tribute series are good enough to start off on. The Standard and Traditional series sport slightly better wood selection and electronics. It all depends on your budget really.