Direct claims are down to the vet, but some vets exclude certain insurers - for example ours won't do direct claims for any company underwritten by E&L.
I would second going for a lifetime policy, and check excesses, limits and exclusions with a fine tooth comb.
Eg when looking recently I saw several that seemed great value, but only cover £40 hospital fees, or £500 for an MRI, or wanted 35% excess for pets aged over 8 years.
Petplan seem to be in most cases "the best" in terms of no exclusions and high cover limits, as well as being good payers. However their price reflects that, and you may not require everything they offer.
Others that our clients seem to use frequently are Animal Friends, Royal Sun (which includes Tesco, More Than, John Lewis, etc) and Agria.
I've only recently taken out insurance myself though, so can't comment on them from the owner's perspective!
In the end we went with Purely Pets - they seemed to suit our needs, but wouldn't be great for everyone. (For example they have really strict hip dysplasia limits, which doesn't matter so much to us as ours are cats).