The antennas that Kevin AG6YO describes are single-band antennas. If there aren't many 70cm repeaters in your area, then a single-band 2m antenna should work fine. However, if there are 70cm repeaters where you live, then you might want to think about dual-band antennas. Antennas designed for 2m will often radiate on the 70cm band with an acceptably-low SWR, but with a poor radiation pattern that avoids the horizon, where the repeaters are. If both bands are important to you, then you might consider a dual-band antenna.
I recommend a dual-band J-pole antenna as designed by Ed Fong, WB6IQN, described in a QST article from February 2003. I homebrewed one myself and learned quite a lot about antennas that way.
I must warn you though, it's a fairly advanced project for an antenna homebrewer: I had to accurately measure the velocity factor of a transmission line, completely understand the theory behind a J-pole and how this design was made to work efficiently on both bands (oh so clever!), understand the theory of transmission lines including shunts and stubs using Smith charts, and raise and lower the antenna many times while making measurements during construction. I borrowed an expensive antenna analyzer that works on both bands. The 2m part was fairly simple to build, but the 70cm part required sub-millimeter precision. I probably put 10 hours into the build, but as I said I learned quite a lot about antennas doing so.
But if you just want to get on the air, you can buy one of these antennas from the designer himself on eBay for a very reasonable price: just search for "dual-band J-pole", and click on the listing that mentions Ed Fong. By the way, Ed's design is mounted in a PVC pipe. Of course you could put it in the attic, but also I would think that there are many ways to disguise a PVC pipe outdoors so that neighbors would never suspect that it's an antenna.
If you're curious about the theory, a J-pole antenna is an end-fed vertical dipole. End-fed dipoles have a high impedance, so the J-pole includes a matching network to make the impedance 50 Ω. Being a vertical dipole, it doesn't need radials or a ground plane. It should be used with a choke balun, usually made from eight to ten turns of coax around a suitable form, such as a piece of PVC drain pipe 4 inches / 10 cm in diameter. (Be sure to respect the minimum bending radius specified by the coax manufacturer.) Because this particular vertical dipole is end-fed, instead of being fed in the middle, the coax doesn't need to be connected perpendicularly to the middle of the antenna; the coax conveniently connects to the end.
People often build (single-band) J-poles out of copper pipe; the antenna then looks like a letter J, that is two parallel vertical lines, one short and one tall, connected at the bottom. The tall part of the J is the half-wave vertical dipole plus an approximately quarter-wave matching section, and the short part is the nearly quarter-wave matching stub.
A dual-band J-pole makes an excellent 2m and 70cm antenna, but there are lots of other ways you could go. There are several commercially-made dual-band antennas that would serve you well. A dual-band antenna made for a car would need a ground plane such as a large piece of sheet metal, so I'd recommend a dual-band antenna designed for home use instead. If you're determined to homebrew antennas, but you want both bands, but you want a simpler antenna than Ed's design, then you could homebrew two single-band antennas and connect them together with a duplexer.
I think you're taking the right approach to get the antenna right first, and then worry about getting a better radio later. Good luck and have fun!