Greg:
I come from a long line of cheap car buyers, and I respect your approach. I may never own a new car again.
The $5,000.00 threshold is significantly limiting, especially in the current marketplace for gas-sippers. You may find, however, that careful selection can save you enough on one car to more than make up for a modest difference in gas mileage. Example: you can get stellar mileage from a Prius, but you might have to drive it 300,000 miles to recover the extra purchase cost. Also, hybrids are great city cars, but essentially lose their advantage in mostly-highway use.
For pure efficiency, Henning's right- you cannot beat the VW diesels, and I can vouch for them being excellent road cars. CJane has a Jetta (1 generation back), very nice ride and drive, plenty of room for driver and passenger (back seat, with the likes of you in front, would be tight!).
Most important thing to remember- at the price point you are targeting, all stereotypes of what car is best (i.e., the ubiquitous "you can't lose with a Toyota or a Honda," etc.) are useless. You are looking for a car which can meet your needs, and has been cared-for well. At that price, you are much more likely to find a car with decent life left in it if you focus primarily on domestics.
Do they use salt on the roads where you are? You might need to look in the south, and use a jumpseat to get there.
I have a dealer I use for used-car selection- he is not a stocking dealer, but rather, he gets your specifications, and attends dealer auctions (where most cars change hands between dealers) and buys the cars with a fixed-percentage commission. Works very well if you know what you want.
The suggestion above of a late-90s or newer GM with the 3.8L drivetrain is good advice; they are well-engineered, amazingly efficient and usually cheap to buy. Mileage is better than you'd ever expect, with 30 mpg readily achievable if you drive smoothly and have gas which has not been tainted with ethanol (with ethanol, deduct 20%). Shucks, my Cadillac Deville (2001, 4.6 L V8) gets a solid 27 mpg if I just set the cruise on 78 or so and keep my foot off of the gas. 22 mpg with government-foisted ethanol-contaminated pseudo-gasoline.
Let me shop for some good exemplars...
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Edit: I agree with Henning's assessment of the Caliber (although it would not fit in the $5k limit anyway); something about the way the CVT works makes it feel as if it's never happy.