I'm not understanding the negativity, because I find 30-34 foot non-slide type A gas motorhomes anytime I check the market. They are often less expensive than smaller C's of similar age, because the demand for C's is greater and non-slide A's are really hard to sell.
Age range is going to be 15-20 years to get that price. In most brands, you have to go back more than 10 years to find A's with no slideouts, the slides have been an A buyer's "must have" at least that long.
My favorites for value in that age and price range are early Bounders and maybe a little newer, Fleetwood's lower price Storm and Flair models. The Bounders were among the first modestly priced A gassers to have generous basement storage, tankage between the frame rails and floor in a heatable enclosed space, and bus like styling replacing sloped front ends. For other tan Fleetwood in that era, I like Winnebago Brave, maybe the upscale Adventure (price differences between model lines tend to shrink with age).
To get prices you want, and readily find no slideouts, you'll be looking at middle to late 1990s, maybe even a bit earlier, and into early 2000s for entry models like Hurricane or Coachmen Mirada, which may not have the basement storage of a Storm or Bounder for non-slide models. For most of this age range, you'll be finding 454 V8 on Chevy (later Workhorse) chassis, and 460 V8 on Ford chassis. Engine tunes for medium duty truck models (i.e. motorhome and panel van chassis) in this era were not as powerful as today, but adequate for the lighter motorhomes they powered, but not particularly economical. Getting into to late 90s, Ford replaced the 460 with a slightly smaller high-tech V-10, and when Workhorse took over the medium duty chassis business they replaced the 454 with a Vortec engines (7400 then 8100) using more advanced electronic fuel injection. But that may be too new for your budget.
With a $20,000 budget, I would be looking for a $10,000 to $15,000 going to the motorhome purchase, using the rest of the budget restoring it to the reliable transportation you seek. What is old enough to fit into your budget is likely to need some work, either because it is well used or has deteriorated from non-use. These RVs come on the market in this age and price range often because someone has decided their money would be better used upgrading to something newer, rather than put into what they already have. People don't fix up old RVs to sell them.