Hi Matthew,
Welcome!
Your question is really a tough one. The problem is that just about every mount has their gems and dogs -- and the only answer is to do the research so you can take advantage of the gems and avoid the dogs.
You first have to determine what and how you want to shoot, and choose lenses that will meet your needs. The vast majority of 35mm SLR lenses will be telephoto, ultra tele, or super tele on the Q because of the extreme 5.58x "crop" factor (8.5mm is "normal" for the Q, but an ultra ultra wide on APS-C or 35mm, and very unusual -- and certainly not cheap).
I'd suggest that you explore local sources first, since in-person you can examine the lenses before you commit to purchasing them. If you have B&M camera stores in your area, this would be a good place to start. Pawn shops, resale stores (Goodwill and such), and especially camera shows and swap meets can also be sources. Just visit and look around and ask questions. You'll find which mount types are the most commonly available and get a good idea of pricing.
Do the research!!! There is an abundance of information on lenses on the 'net. It can be very specific, so you need to be very detail-oriented to really make the best of the information that's out there. A good example of how specifics can make a difference is to look at the Vivitar Series One 70-210 zooms. There were, IIRC, 5 different variations, and 3 manufacturers, and they range from mediocre to excellent optically depending on the variation that you get. This is pretty much the extreme though, and in OEM lenses (offered by the camera mfgs), there are fewer variations, and you can usually get a good idea of the optical quality of a given lens from the user comments posted on various sites.
Personally, I shoot Pentax DSLRs, so the choice is pretty simple -- K mount lenses, so I can use them with my DSLRs. I already have a pretty extensive range of lenses since I've been acquiring them over the past 7-8 years. If you may consider getting a DSLR kit in the future, this might be a consideration for you -- get lenses that will be compatible with the DSLR that you'd most likely choose. Be aware that with all of the other brands (Canon, Nikon, Sony [Minolta], Olympus), the older manual focus lenses might not be compatible (might not control aperture, might not meter, or might not even mount) with (at least some of) the DSLR bodies so this might be another area to research. With Pentax, it's easier because Pentax DSLRs will be able to use just about any lens that was made to fit any of their cameras, past and present (sometimes an adapter is needed though).
In the Q system lenses, I can wholeheartedly recommend the 01 prime, the 06 tele zoom, and the 03 Fisheye -- all top quality lenses IMO. The 02 wide-tele zoom is only competent IMO, and right now, the best alternative if you want to shoot wider than the "normal" (captures a scene pretty much as you see it) 01 prime.
Congrats on getting a Q -- you are obviously a sensible person
. Have fun with your new camera. . .
Scott