The size of the keyboard generally dictates the number of bass buttons that can be fitted in an instrument. Common keyboard sizes are 26, 30, 34, 37, or 41 notes, which is sometimes regarded as "full size" All accordions have more narrow keys (20mm) than standard pianos, and some accordions have still smaller keys (15 - 19 mm) which are suited to smaller hands, these are sometimes called compact models.
Choose an instrument carefully with regard to what music you may want to play both in the short term and forseeable future. It's always a trade off between specification, portability, and price. I wouldn't recommend accordions with less than 26keys/48bass as you will probably run up against it's limitations very quickly.
The following table shows how the number of right hand keys / left hand bass buttons restrict the type of music you may want to play. The number shown (%) indicates the percentage of tunes PLAYABLE in a selection of popular music albums.
It's meant to be a guide, not a definitive assessment of all publications and music genres.
So the above table shows, for example, that if you want to play klezmer on a 48 bass/26 key instrument, you'd be restricted by the right hand keys much more than the bass.
I haven't included 37/120 models or larger as you can handle pretty much anything with them.
A 26/48 model is great for learning and if you get a decent one you'll probably want to keep it for portability even if you upgrade at a later stage. A 34/72 is a great compromise between portability and versatility.
Bear in mind that with a 60 or 72 bass accordion, whilst all common chords are represented, it's not necessarily easy to play in all keys as, for example, F sharp is at one end of the button board, but C sharp (D flat) is right at the other end.
Voices or number of reeds
Another choice you're faced with is the number of sets of reeds in an instrument. Very few models have just one set, most have at least two in the right hand. To get the vibrato sound often associated with accordions one set of reeds is tuned a few Hz higher than the concert pitch set. To get a more pronounced vibrato a third set of reeds is often tuned a few Hz lower. Many three voice models have the third set tuned an octave lower instead to give a thicker, darker, sound. Four sets of reeds make all the above possible or the fourth set can be tuned an octave higher than the concert pitch, this is usually called a piccolo reed. Terminology like "oboe" "bassoon" "violin" etc on the stops is rather unhelpful - you just need to understand what pitch reeds you are using and which are detuned in what direction. Sometimes you will see LMMH standing for Low, Middle, High reeds or 16' 8' 4'
If you have to have everything there are 5 voice models which weigh around 12kg.
On the bass side usually four sets of 12 reeds are used to cover the range of notes and chords. Another set of reeds tuned an octave above/below give the possibility of a few changes of tone colour.
Note that the number of reeds on bass side is not related to the number of bass buttons.
As if that's not enough there are a variety of ways a pair of reeds can be tuned ranging from "dry" - where the reeds are tuned as close as possible to "wet" where they are tuned as far apart as is bearable. If you are ordering an instrument it's as well to get it tuned the way you want.