NorthStar,
Unless someone is willing to spend gobs of money, there is no single antenna that will cover all bands really well. Since 'cheap' is nice, and if a person is willing to put up with less than "best" performance, there are a number of possibilities. Just depends on how much room you have to 'play' antennas with.
One of those 'cheap' possibilities is a 'fan' dipole. A number of 'resonant' dipoles all fed from the same feed point. Or a number of dipoles hung all over the place with separate feed lines. Or a single wire as long as you can make it, with a very good ground system.
If you aren't too adverse to using a tuner, there are a lot of things you can make work in a lot of different places. Just depends on the tuner and what you use for a feed line. (There really are other kinds of feed lines than just coax.

)
What's the most common HF antenna around? The everyday el'cheapo dipole. They work remarkably well for most bands, don't cost much, are fairly easy to make and put up. The hardest part is keeping the "significant other" happy, sort of. None of that even gets into vertical antennas, so there's a whole 'nuther ball park to play in.
The worst part of the HF bands is that the lower you go in frequency the bigger/longer the antennas get. Not a whole lot you can do about that with out a compromise or two to deal with, and not really all that hard to put up with if you have to.
What would be the best advice to give a new General? Start simple, don't expect miracles, and try different antennas when you can, or feel like it. The old saying about as much as you can and as high as you can really does hold true in most cases. Half the fun of it is trying something new anyway...
- 'Doc
(I like loop antennas a full wave length on the lowest frequency of use, ladder line type feed line, and a good tuner. It won't do everything, but neither do I, so what else is new?)