"Does every expansion have cards unique to it or do they get duplicated in other sets"
99.9% Unique
tldr: get Druid vs necro first.
I just got them chronologically, but I think they differ in quality. I got conquest of kumenjaro(COK) first and i either like it the least or consider it part of the core by now. its the least school-focused of the expansions(according to me), so it has a few cards for everyone.
I would start with the expansion which offers schools/mages which appeal to you. If that fails, start with Druid vs Necro since its the best one
. I'm biased because I love the druid, but Arcane wonders did a podcast on what to buy, and they rated D v N high too
Don't get forged in fire until after you get forcemaster vs warlord(FvW) unless you want to proxy a few cards(barracks and standard bearer for example). FIF or FvW alone is a warlord with limited tools(though the other mage in each respective set is fun). I believe FvW is out of print, but I found its warlord too underdeveloped until FIF came out. The forcemaster is pretty fun though. I'd say FvW is better than COK, but it probably costs twice as much, and you stated that price is a factor.
arbitrary order: Druid vs necro-> conquest of kumenjaro -> FvW ->FIF
Dominion is coming out soonish so if you arent buying immediately, check that out as an option.