No worries @Saraku ! Fundamentally speaking the subtype of your shamisen matters very, very little - unless you have a particularly strict teacher.
Generally speaking (and to the best of my current knowledge), Kouta and Hauta shamisen are essentially the same! The biggest indicator for the intended genre are the accessories found with the instrument when purchased on the secondary market.
The presence of a particularly wide, tall koma and no bachi generally suggests a kouta instrument.
The presence of a more standard koma and a nagauta style bachi (whatever the size) generally suggests hauta or perhaps utazawa.
Still, the intentions of an instrument matter little when compared the intentions of the player. So worry more about what you want to do with it than what its previous owner though of it :p.
Fundamentally speaking, your shamisen is on the smaller end of the spectrum.
A go-rin-dai body is just ever so slightly bigger than a nagauta, and so will tend to be lighter and brighter than its larger cousins. This is the same size we generally use in min’yo, incidentally!
A chuuzao may be more or less comfortable for you to use compared to a thinner hosozao or wider futozao. It doesn’t impact the sound overmuch.
A hatomune will make playing the highest positions of your instrument very difficult if not impossible - but those positions are only rarely used in regular songs.