I agree with Sas, some will fruit first year with good care, but most likely just to be on the safe side I would say count on 2 seasons before fruit, and rarely it might take 3 seasons depending on the cultivar.
From what I'm seeing even a few renowned slow growers, like for example Figo Preto, want to put on figs first season from cutting, but fast growers such as Kathleen's Black are showing no signs of figs even with 2 seasons of growth...but the seasons not over yet.
In answer to your other question, if you don't want to start with cuttings, I would get the largest size your comfortable with so you have the most roots and hopefully healthiest start, so at least 4" size, which is essentially a rooted cutting. I have found those figs that are slow growers to start will generally stay slow growers.
I have never ordered from there, the only caveat I can see with a smaller pot is smaller shipping costs, that's it no other advantage. I would ask them which cultivars they have that are known to be the most precocious.
"If yes, is there a problem getting them this time of year?" Heat during transport maybe?