Used bikes are quite a bit more expensive and thinner on the ground in the USA than here, Nebulous. What I would be more wary of is if it was a "proper" TLR or a Reflex
Don't get confused with 4 stroke terms, there is no sump oil, only gearbox/clutch oil. The mains and big end get their lube from the petrol/oil miix, aside from clutch side main which is lubed by gearbox oil.
If you're on a budget take a look at the Wulf gear. Very reasonably priced. I after something a bit more fancy have a look on e-bay, I bought a brand new Airoh TRR carbon fibre helmet for almost half the retail price as it was last years colours!
Look on the South Eastern Centre website, there is a list of clubs and events shown there. There is also a new North Kent Trials website, but is very new and still under construction
I see you live not a million miles from me. I am curious as to the practice ground you allude to? Only a couple spring to mind (Farnborough & Horsley). Fuel capacity of a trials bike would be one concern, also tyres as you already say. Not to mention wear & tear on the bike as they are not known for their top speed let alone the uncomfortable seating position. Back in the 70s I remember one young lad that used his bike as a sole means of transport and also rode it to and from events! Needless to say the mechanicals didn't last too long.