Edit: Aha ... three of us typing in parallel

The most direct route would be the National Express bus from LHR bus station to Woking, followed by a direct train to Yeovil.

Annoyingly, South West Trains only seem to have FastTrack machines at a few major stations, e.g. Waterloo or Reading, which both involve taking an indirect route.

You don't say whether this is a single or return trip, or how long you're staying, but there may be little or no value in booking in advance if the walk-up Saver fare is the same or only slightly more than the advance purchase fare, and you can take the more direct route.

There are thru fares from LHR to Yeovil via Woking, but I don't know if these can be purchased at LHR.

I'd just turn up & buy the bus fare at LHR (or online - you can get an e-ticket) and then buy the train ticket at Woking. You're unlikely to need a seat reservation outside of the rush hour, which would be the only other incentive to book the train in advance.

Useful links:

National Express coaches
National Rail journey planner

I'm sure stut will be along soon to add more

hth