A few points:
1. If the two people haven't already, get a Two Together Railcard. Costs £30 from any station (two passport-sized photos are required), will pay for itself several times over for this trip alone and is valid for a year.
2. For the best 1st Class facilities/service you'll want to take an itinerary that involves Virgin from Liverpool to Stafford and CrossCountry from Stafford to Bristol. There'll be a reduced service on Saturday though. There is quite a nice 1st class lounge at Liverpool Lime Street but I don't think it opens until 8am on Saturdays. Suitable itineraries could be:
Saturday 2nd July
dep LIV 07:47
arr STA 08:40
dep STA 09:00
arr BRI 11:09
Monday 4th July
dep BRI 15:00
arr STA 17:00
dep STA 17:23
arr LIV 18:21
3. Split tickets
Off-Peak 1st Return, Liverpool Stations to Wolverhampton, route VIA CREWE
2 adults w/ 2TR discount: £60.20
Off-Peak 1st Return Wolverhampton to Cheltenham Spa, route ANY PERMITTED
2 adults w/ 2TR discount: £83.20
Anytime 1st Return Cheltenham Spa to Bristol Temple Meads, route ANY PERMITTED
2 adults 2/ 2TR discount: £55.70
TOTAL £199.10