TA, I fly HF very frequently to the Canaries (four hours max) and never had a problem with HFs 738s or A310s (I have always been on their A310s to the Canaries). Their service is better than a comparable LH european flight, i.e. Frankfurt-Cyprus with the same length.
HF has not connection to STAR at all, if you want this, use Condor, will give you miles on LH (dont know if this will give you miles on any other Star mileage program) but no status miles.
Condor plan to introduce "comfort class" to the Canary islands from this summer, and I think they will start this on the routes to Tenerife in their 757s.
Most options to go to the canaries are from FRA. If you dont want to use a charter airline, your only option is IB via Madrid, and I can assure you the service level is much lower than any German charter airline (-: