There are a range of good used low cost dual sport bikes available, but for the OP's stated purposes and budget you just can't beat the Suzuki DRs.
Look for an early decade electric start DRZ400S (street legal model). The original DR350 series was a great bike, but kick starting them gets old, even after you learn how to do it with one kick every time.
If you live in a state where you can street license them and want to do mostly pure dirt work, then consider the DRZ400 off-road dirt model.
The later model DRZS (street legal model) all have the upgraded off-road model forks, etc. and are more capable off-road, but the early decade era bikes will be fine with a cartridge emulator and shock upgrade.
The street models are heavier stock, but by the time you take all the unnecessary stuff off of them the delta is pretty small. Drill a few grease zerks and you'll be hard pressed to tell the difference without disassembling the forks, assuming you don't notice the enduro computer that is stock with the street model.
Put a set of DOT knobbies on it and go have fun.
The 350-400 DR series has a motor that just won't quit. If you change the oil & filter regularly they are pretty much indestructible.
It's a much better all-around (meaning everything short of dirt competition to freeways) dual sport bike than the Suzuki DR650 or the Kawasaki KLR650.
The early 2000s Yamahas were more competition oriented bikes, very fast and capable, but not well suited to the typical owner neglect / long duty cycles of dual sport use. (insert Yamaha fan ALL CAPS flame response here) You could say the same for KTM. (repeat flame insert, change logo to KTM)
For height challenges, drop the triple clamp and change the shock preload. I've also cut down the seat. The ultimate solution is to change the rear shock lever arm. You can do a LOT of height mods to the DR right out of the Suzuki parts bin.
And make SURE you do the carb vent mod on the CV street carb. It solves all of the hard start problems when you dump it with a hot engine.
You can buy an early decade used dual sport bike with a better stock suspension, lighter weight and more off-road race wins than the DRs, but you'll never find one with a more reliable, stump pulling motor and arguably more tolerance for owner neglect and abuse.
