Have a look at the Gobur folding caravans, we were pitched next to one last year and it looked great, it only took them about 20 minutes from arrival to kettle on, they're about 900 to 1000 kgs and tow easier than a caravan, and being insulated good for all year use. There's a few used models in your budget on the manufacturers website
here iincluding one with heating etc.
I suspect the problem you may have is if you want 3 berths, most of the small caravans are 2 berth (although we put our 6 year old on the floor). However some trailer tents are 4 berth, we started off with one and managed to cram us and three kids inside and had some great holidays, including a couple at haven sites, you will easily find one in your budget.
The best things is to go and have a look at a few just to get an idea of what you really want before you a finally commit to buying anything.
Then research what to look out for when inspecting and take great care to make sure everything's in good condition.
Finally don't forget that unless you find someone who's selling a package there's a lot you'll need to buy on top of the van / trailer (water carriers etc), Initially you can take cooking stuff etc from the house, but you'll soon get fed up with that and want a separate set.