20k budget...
I'd go for a 6.0 in the 15k range & plan on another 5k for heads/studs/updates. If you aren't afraid of turning a wrench it's a pretty easy engine to work on. Stud it & dump the egr (if you dont have emissions testing). While this is a pretty big job at first, do it once and be done with it. If you do decide to go with the 6.0 I cannot stress enough to do your reading and I mean a lot! The 6.0 section on the forum has a mountain of information on buying and repairing them.

Also if you plan on getting a diesel, get a scanner of some sort 1st. It's the MOST used tool any powerstroke owner uses. TorquePro or Forscan app for your phone & a Bluetooth obd2 adapter are the cheapest route($20-30). Also when shopping for the new truck it'll let you know the health of the engine that the useless gauges dont show you. It amazes me that there is still useless analog gauges in vehicles nowadays for the outragous price of them.

 

My 15' F250 4x4 6.2 gets 14-16 mpg on the Hwy.
My 16' F350 4x4 6.7 gets 14-16 mpg on the Hwy.

Our 15' 6.2 tows our 9000lb + Travel Trailer without an issue. Don't confuse the 6.2 with the 5.4. Different animals. We are selling the 15' and our TT. We bought the F350 to carry our new Lance 1172 Truck Camper.
If it weren't for the fact I need the Power and Ability of a Diesel Dually, theres not a chance in Hell I'd own a Diesel.

 

My next pickup will be a F-250 with a 6.2 gas. They are hard to find around here, so I'll need to travel a ways.

Actually, the dealer had some leftover 16s crew cab 4x4 with 6.2 gas for $37,000. I don't want that steep of a payment.