The ionosphere doesn't reflect VHF and UHF signals, which allows earth stations to communicate with satellites, but the ionosphere does tend to unpredictably rotate the polarization of signals passing through. The worst-case scenario is that you have an linearly-polarized antenna oriented 90° from the polarization of the signal (e.g. you have a vertically-polarized antenna, but the signal is horizontally-polarized), which would attenuate the signal by about 30 dB. For that reason, permanently-mounted antennas (on moving aimable mounts) for ground-earth communications are almost always circularly polarized. (If you plan to hold the antenna by hand, then you could rotate the boom of a linearly-polarized antenna to maximize the signal.) Circularly-polarized antennas can be polarized clockwise or counter-clockwise (or anti-clockwise if you prefer). This AMSAT web page says that the polarization can switch during a pass, so being able to switch the antenna from one circular polarity to the other can be useful. (I didn't know that.)
Amateur radio satellites often have enough gain that a simple antenna such as a quarter-wave vertical can be enough for the earth station. I'd think that cubesats would use much less transmit power than amateur radio satellites. An antenna with more gain than a discone would probably be optimal.
AMSAT is an organization dedicated to amateur radio communication with satellites, and they have a web page about cheap satellite antennas that hams can build here. Of course you may need to communicate on other bands, and you may not have the skills or equipment to "home-brew" your own antenna; if you're on a tight budget and are limited to commercially-available antennas, then I'd recommend a linearly-polarized yagi on a handheld boom, with the boom rotated to maximize the signal. If you are open to making your own antenna, there are many online articles about building ham-band satellite antennas. Antenna designs typically scale well, so a design for one band can be adapted to work on double the frequency, for instance, by halving the size of the elements and the spacing between the elements.