Given that the vast majority of amateur cubesats transmit on the 2m and 70cm bands, a dish (unless it’s a really big one) is not the most practical way to go. Someone else can probably do the comparisons on how big a dish would need to be to provide the same gain of a ‘reasonable’ sized yagi antenna.
There are amateur satellites with S-Band (2.ish GHz) downlinks, but these are few and far between.
I’m not an expert on radio stuff, but my feeling is that going for a UHF dish would be too big and too expensive. The truth is that there are not many S-band satellites right now, but their number increases month by month as there is a need for bigger transfer rates. For example in the SSO-A launch I can see 5 from 22 cubesats having an S-Band transmitter.
So, my suggestion would be to go for an s-band dish and uhf antenna on the same rotator (or different) which probably would be on the same cost of a big UHF dish.
Look for on-line antenna calculators.
for a parabolic if you want to know gain, the simplest you input diameter and frequency and get
a gain figure. Easy, and simple and not totally precise. You will often get also the beam width.
As youi get bigger, the gain goes up but the beam pattern gets narrower ( the two are interrelated)
when you have High gain eventually your challenge includes need for precise tracking, more so than when the gain of (whatever) antenna you use is small. Here is a calculator that I found, easy to use that gets you started.
Just plug in a hypothetical frequency, like 437.5 mhz or 2.4 ghz and see what you get. Then, compare gains when you double the diameter of the dish, or halve the size of the dish, see also what happens to the size of the beam. Write results down. do this a lot to get a feel for what is happening. Eventually you will be able to have in your head gain figures and beam widths for some example parabolic antennas, and example frequency bands. And eventually you can make in your head close estimates for any parabolic antenna, at any frequency.
Then, look for a similar on line calculator for Yagi Antennas. for these you vary the number of elements.
and then look at gain. and beam patterns. different calculators have different amounts of simplifications
but for ball parks calculations there are many that will work…