K Body, Q Body and "Lithium ion" body, can anyone tell me the differences between these?
Q mount is a not very popular small sensor ILC mount that Pentax developed and, I think , still sell. It's not compatible with SLR or DSLR lenses. Forget it entirely - most people have.
K mount is the generic name for the Pentax SLR/DSLR mount.
It has evolved over the years but with possibly a handful or rare exceptions you can physically mount and use any K mount lens on any Pentax DSLR.
The PentaxForums.com website has extensive information on the K mount and most things Pentax.
I've used both Pentax film and DSLR bodies and I've used ancient (but lovely) 50mm f1.7 'M' lenses (the original bare-bones K-mount fully manual) on my K100D and K10D without problems.
Note that Ricoh (long ago) used a version of the K-mount which you'll sometimes see lenses with. These lenses should be avoided ! They can "lock" into the body and be very hard to remove.
Most Pentax bodies have a way of metering (or forcing metering) with even the most basic M lenses (of course you still have to set the aperture !).
"Lithium-ion" refers to the fact that many Pentax DSLRs can/did use rechargeable AA batteries instead of proprietary lithium-ion batteries. At least one model (maybe more) can use either.
Typically lithium-ion batteries have a larger charge and some people don't like AA's. However you can't just run down to the supermarket and buy a spare Pentax lithium-ion battery for your DSLR in an emergency, whereas you can buy precharged AA NiMh long-lifes (like enloops) all over the place. As flashes often (always ?) take AA's I prefer them myself as I can pack a bunch of them in my kit bag and I'm good to replace whatever I need quickly (and a small recharger lets me replenish them from a wall socket).
Also, which would be a decent pick 2nd hand as a solid basic digital body? I don't need bells & whistles or "more megapixels".
Avoid the K110D because it has no sensor based stabilization. I'd avoid the older pre-K models as well for the same reason (although they're all good solid stills cameras otherwise).
Avoid the K-x DSLR if you expect to mount manual focus lenses or want to use manual focus. The reason for this is simply because Pentax removed the visual focus confirmation in the viewfinder from that model. It's otherwise a very nice DSLR with (I think) the same sensor as the Nikon D5000 but the much nicer (IMO :-)) Pentax handling.
Before I'm assassinated by Nikon fanboys, I did own a D5000 and I liked it, it's just that for me the handling on Nikon's never felt as natural as Pentax models.
If you don't need megapixels I'd consider any other Pentax DSLR. For a modern level of good ISO and dynamic range I'd suggest something from the K-R onward, but if you're OK with pre-D5000 levels of ISO and dynamic range (and I shot a wedding a few years back with a K10D) I'd go for a K10D, K200D or K100D. The K200D is basically a cut down K10D, but is water resistant (!) and uses the same sensor as the K10D. The K100D is only 6Mp but as it was the first DSLR I felt entirely natural handling, I have a soft spot for it. Took some of my favorite personal shots with it as well, including some with my beloved Pentax 50mm f1.7 M.
An alternative approach is to grab a MILC, ideally one with focus peaking and a decent EVF, and use a simple adapter to mount you Pentax glass.
The MILC approach has an additional advantage : you can use focal reducers to restore the full frame use of your lenses (as most Pentax DSLRs are crop frame). I've done this myself with a Sony NEX F3 and both dumb-simple adapters and focal reducers (cheap eBay ones). A very satisfying way to shoot if you're good with manual focus (which is OK with focus peaking). Handling is quite different from a DSLR, but it was a painless adaptation for me.
The MILC approach is quite good for fun. I'd probably avoid it for anything serious (indeed I did avoid it when I shot that wedding with a K10D, as I had been using my NEX for quite some time).
I'm not really a video person so I have no real idea what video capabilities the Pentax bodies have. If you need video I'd grab a Sony NEX MILC or possibly a Panasonic GH model if you're OK with the smaller sensor.