>>193748Any GPS will work for geocaching. There's also apps for smartphones that do the same. Or just use lat/long.
Garmin eTrex is a good basic GPS. These can be found for under $100 on craigslist or ebay.
At the upper end of your budget, look into the 60- or 76-series receivers. They're a lot more powerful and have more features, with mapping and better computer interface capabilities.
I had a 60CSx, after 5 years it finally gave up and I grabbed a 76Cx for $150 to replace it.
Also factor in the cost of maps and accessories/mounts. Garmin's maps can be ~$100 (CityNavigator-North America is about $80 iirc); sites like gpsfiledepot and openstreetmap do offer some maps for free but the quality and coverage is hit-or-miss.
RAM-mounts are the only way to go for mounting the unit. Plenty of options to put it wherever and on whatever you want to put the GPS. Expect to spend ~$50 for a complete kit.