Hello. It's nice that you are interested in Georgia. All four seasons are beautiful in Georgia. It depends on what your priorities are. In winter, you can visit winter resorts such as Bakuriani, Gudauri, Goderdzi, where you will find snow and ski slopes.
Spring is also very beautiful in the capital, when the trees begin to bloom. In summer, you can visit cities bordering the Black Sea, such as Batumi, Tsikhisdziri, Kobuleti, Ureki. By the way, there is magnetic sand in Ureki where people come for healing.
In autumn, Kakheti is very beautiful, where peasants harvest grapes, crush them and then make wine. There are special places for tourists where you can participate in this process. In addition, the nature of Kakheti in autumn is beautiful.
If you want to see the whole of Georgia, with its sights and monuments , then I recommend visiting Georgia either in the second half of spring or in the first half of autumn, when it is neither too hot nor too cold.
As for groups, there is a group on Facebook called 'where stay in georgia' and 'მოგზაურთა კლუბი - Cheap Travel Georgia'. There must be many more groups, I just don't have the information. I wish you good luck.