Cheap is all relitive. In 1992 I bought a cheap Cherokee 235 for 25k, 6k later I had a pretty good airplane. 4 years later, after a catastrophic engine failure. I got to put a new engine in it. Lost my a$$.... Also during that time I owned a flight school/flight club with all leased airplanes.
for a little background information, an FBO doing lease backs is looking for two types of aircraft. The first type is a good trainer. C-150/152, C-172, PA-28...... The operating costs are low, they can fly the P*** out of them without worrying about heavy maintanence. The second type FBO's are looking for are airplanes that people will rent for pleasure. C-182 (RG), PA-28R, sometimes a PA-32 or C-206. In rare cases someone will lease back a twin, but this is usually a money pit for the owner.
These are the most standard aircraft at FBO's. Some places will get into speciality stuff like Champs, C-120/140, short wing Pipers, and such. But insurance costs and min pilot requirements usually make these prohibitive.
Ok now that I have digressed significantly, I'll get into the advice catagory.
If you want an airplane that is inexpensive to operate and can be leased back, I'd suggest a 152, an older 172, or a Cherokee 140. Stay away from the odd ball stuff. Piper Tomahawks, Colts, Tri-Pacers, C-175's, and Tri-Champs all fall into the odd ball catagory.
If you want an airplane which you will keep for a long time and own it because you really like it, then all bets are off. Buy what twists your tail.
I hope this helps you figure out what you are looking for. I also suggest buying a current copy of Trade-A-Plane or Aero-Trader to get an idea of price ranges.
Oh yeah, the cheapest to operate and easiest to maintain airplane I've had contact with, is the old Ercoupe. They can be bought for less than 15K, burn 4 gallons of mogas an hour, and are really fun to buzz around in. I think there is a wing spar AD, but if that has been complied with, you are pretty much home free.
Another thing you have to consider is what you want to do with the airplane after you buy it. Do you just want to build time and have fun with it, do you want to go on to get your instrument rating with it, is it something you want to keep for a long time or get rid of when you build some time. Those are all questions you have to ask yourself. If you just want to fly VFR and have fun flying low and slow then I would recomend getting something like a Cessna 120/140, Aeronca Champ, Luscombe or other taildragger. If you want to get your private, bulid time, get your instrument and build some more time you might want to look into a 172, Warrior or Archer depending on how much you want to spend. Any of those airplanes would also make a deacent x/c airplane so you could take your wife or girlfriend on a trip every now and then. You are going to become a better stick if you would get a taildragger and fly that around for a while especially a Luscombe or 120/140. Good luck to you in whatever decision you make.
I purchased a 62 Cherokee 150 for 19K and put about 5K into it ,flew the hek out of it for 2 years and sold it for 23K. In the end I came out ok, but along the way there were more headaches than you can imagine- unexplained engine problems, mechanics that take advantage of your wallet, expensive parts, and the stress of knowing what a major engine problem can cost you.
You may want to reconsider the lease-back option of your plan. I purchased an aircraft and did the lease back thing and it worked out fairly well till the IRS got involved. I researched the the tax laws before I went ahead with my little venture and sought out credible advice from an experienced accountant before I started. Heres what the problem was: The tax laws changed midstream and the IRS now considers lease-backs where the owner is leasing to a flight school a passive lease. With a passive lease the IRS does not allow year to year depreciation write offs like in the past, instead it is only allowed after you sell the aircraft. One lump sum instead of 5-20% write offs. Taking this in to consideration it made it really tough to afford the cost of the lease back because most places make the owner responsible for the maintanence costs as well as insurance. The best scenario I found was that the lease-back broke even and the time the flight school took off my engine was not worth it.
As far as decent timebuilding aircraft are concerned try to buy something that makes a good instrument trainer such as a Cherokee 140 or a Cessna 172, there plentiful and can be had inexpensively if you shop around.( dont buy a Cessna 172 with the old O-300 its expensive to rebuild and O-320's are much more plentiful.)
my 2 cents Woody
We're uptown up here on the north slope. No need to light preheaters, just pulg in the airplane and throw on the engine blinkets. The sled even has an electric heater in the cabin. Warms it up to 15 below from 30 below. Tee shirt flying weather....
One option that I would suggest that might work very well for your scenario is to look for a flying club in your area. There are a lot more pluses then there are negatives such as:
1. shared maintence expenses
2. cheaper insurance
3. the ability to fly a nicer airplane then you might afford on your own.
4. usually a nonrenter mentality attitude when others also have a little of there own fat in the frying pan.