For an easily homebrewed dual-band base antenna, it's hard to beat the all-aluminum Arrow J-pole. The design is on the web. Allan Lowe from Arrow has put the plans up at:http://www.krell.com/amateur/antenna/jpole/
But I wouldn't use it for satellites. There are better alternatives.
Let me correct some commonly quoted misinformation about working the "easy" sats. You really don't want to get your signal going *up* to work the Low Earth Orbit (LEO) satellites. The main reason is path loss. You need quite a few dB more to hear a satellite when it is near the horizon, because the signal is passing thru thousands of miles of atmosphere. When the bird is near the zenith, you get as much as 12-15 dB more signal.
Now couple that with the concept (easily forgotten) that a LEO satellite is RARELY near the zenith anyway. When the bird is near the horizon, its apparent motion relative to your position is quite slow (because it is moving mostly toward you or away from you); when it is near the zenith, the apparent motion is quite fast (because it is moving PAST you at 17,500 miles/hr).
I modeled two full weeks of six-a-day UO-14 passes at my QTH by using a tracking program and sampling the satellite track every 15 seconds. I found that the average satellite elevation here during a pass was 14 degrees above the horizon. That includes the passes where it goes straight overhead, but as I said, its apparent motion is quite fast at that time.
That's pretty much what's wrong with W4RNL's Moxon turnstile idea. I built one of these, and it wasn't a particularly outstanding performer. Why? because it looks mostly up at high angles, when you really need the signal at *low* angles. Dr. Cebik is a brilliant man and has some GREAT information on his site--when building my station I couldn't have survived without him--but the concept of using a Moxon turnstile design for satellites was a little off. If you have to use a fixed antenna, K5OE's Eggbeater II design is more appropriate (lower radiation angle) and just as easy to build.
I agree with the idea that an az-el system is the best, however there are alternatives. I earned my satellite VUCC on the FM satellites using an HT for 440 receive and a 2m mobile rig for transmit. I built a little handheld 4-element yagi for the downlink antenna (mounted a Ramsey preamp and 9 volt battery right in the handle), and used the 1/4 wave whip on the car for my uplink. A mobile 1/4 wave whip, believe it or not, sends signal at just about the right angle for the LEO satellites. Most of the time I could hit the birds with the mobile set to only 5 watts; using 2 radios gave me full duplex. If you don't feel like homebrewing, it's pretty hard to beat the Arrow handheld antenna. It's pretty much the standard for the FM birds. Handheld antennas are great. When the bird changes polarization on you, you just flip-flop the antenna.
If you have some extra bucks, find a used azimuth-only TV rotor and mount a couple of yagis pointed at a fixed elevation angle. That's what I did when I finally graduated from the HT/Mobile setup. For downlink, I built a circular polarized 440 yagi that had left-hand and right-hand switched with a relay, and just used a vertically polarized 2m yagi for uplink. (remember, the receivers on the satellites are GREAT--they can hear very weak signals; it's the transmitters, typically less than a watt, that challenge you). That's why I did the pass-elevation modeling I mentioned above. A modest yagi is going to have a enough -3dB beamwidth to get you nearly to the zenith if you point it a little above the horizon, and even if the signal is down more than 3dB, you really don't need it when the satellite is that high. I pointed mine at 8 degrees. Even though the average pass was 14 degrees, I felt I needed more gain for the lower portions of the pass. It worked fine that way. And the 2meter yagi was killer into the repeaters if you pointed it at them. I could routinely get into a repeater 120 miles away with it, even though it was pointed up a little.
And DO use a mast-mounted preamp in line with your downlink antenna. Even the little $12 Ramsey 440 preamp (kit built) works great. By mounting it up on the mast, it will amplify the received signal at the antenna where it is the strongest, and will overcome quite a bit of feedline loss. You can't transmit thru the inexpensive Ramsey (it has no RF sense switching), but if you're using 2 rigs that's not a problem. If you're using 1 rig and 2 antennas for uplink and downlink, you'll need a duplexer in line to keep from frying the preamp. But you'll need that anyway.
I wish I had a nickel for every guy I heard on the FM birds that had a great signal INTO the satellite but couldn't hear at all when you came back to him. An inexpensive preamp solves that problem nicely.