Hey! Sorry for the incoming wall of text, just trying to help 
So, when I was picking my first shamisen, it was pretty much all based on affordability and it being tsugaru style, since I knew for certain that was what I wanted to play. Since I’ve gotten more comfortable with the instrument, I’ve upgraded from there, but a synthetic skinned basic shamisen is a great place to get your footing.
However, you already seem to have a pretty good feel for shamisen (even if it’s not a regular one) so it might be advisable for you to go and upgrade a little further than the basic entry level sort.
The sao on a nagauta is about 26mm wide, or about 1.02 inches, so it’s not really that different to what you already have. The skin is naturally more fragile than a Tsugaru shamisen’s, so if you want to play any tsugaru pieces you won’t really get that percussive tatakibachi, but a nagauta skin can hold up fairly well if you treat it a bit more delicately.
If it’s indeed Nagauta you would like to play, the Beginner’s Shamisen in the Bachido store looks great - I haven’t played it myself, but it looks and sounds really good, and to my ears, like a normal nagauta shamisen.
If you want to play Tsugaru, Bachido also offers a variety of higher end shamisen if you want to splurge a bit, but if you want to be more budget conscious, I’d recommend one of the ST model shamisen you can find on E-Bay (http://www.ebay.com/itm/Tsugaru-Shamisen-Sangen-Patent-High-Technology-Professional-ST1-Traditional-JP-/162490550949?hash=item25d5310aa5:g:-MEAAOSwSypY~3j3) like this one.
That’s what I got started out on and while the tone doesn’t really hold up to a real craftsman made shamisen, it’s great for learning the proper techniques and songs so once you get a nicer one in the future all the knowledge transfers right over.
The ones in that series start as the basic ST1 (no azuma sawari) and goes up from there with additions such as an azuma sawari or a naga fukuro, but on all of the ones of that series with the synthetic plastic skin they do sound, well, plastic-y. But, they are a more affordable way to get your feet wet in the world of shamisen.
Again, though, if you are comfortable enough from the kankara you’ve been playing and would like to get the full on Tsugaru shamisen experience, the ones in the Bachido store can be skinned with FiberSen or natural skin, which get a far better tone than the ST series.
I’m not sure if those can, but the high end specialized ones here like the Akatsuki and the Eclipse can also be skinned with Ripple. Both Ripple and Fibersen sound nearly (if not) identical to natural skin.
The sao on a Tsugaru is 30mm, so a bit thicker and if you ask me easier to get your fingers around. The skin is also much more durable.
Anywho if it’s just regular minyo you’d like to play (not specifically Tsugaru) that can really be done on any type, though there are specifically made minyo shamisen. You can find some of those too on E-Bay, but I’d be careful as most of them have broken skin as they are.
And, of course, you can always go through proper shamisen shops like Shamisen Katoh or E-Kameya and see what they have to offer and what you like.
Hope this helps!
