The best way to figure out if your budget is reasonable is to start looking around at what you can get in that price range. I think it might be a bit tight, but not too far off. Prices do vary somewhat regionally. Around here, it's possible with some searching to get basically sound and operational and reasonably reliable motorhomes for $20k or somewhat less...though they aren't always plentiful.
You'll likely be looking at 15-20 year old motorhomes, give or take. At any age, but especially that old, the condition and maintenance are by far the most important things to look at. An unmaintained top-of-the-line RV will be a far worse deal than a well-kept lower-end model.
Make sure you budget appropriately for maintenance and repairs. In particular, if the tires are getting old, figure how much replacements cost; for a typical class C, that might run around $1000, and likely more for most class A's. Most motorhome tires need replacement due to age before they need replacement due to wear or milage.
