A used enoch tradesman isn't out of reach at that budget and will hold its value far better than any gold tone if you decide it isn't for you.

Whoever told you to get a 12" banjo is trying to impose their personal preferences on you, and maybe their concept of “old-time music.” There is no standard. I have a couple of 12” banjos, but prefer 11”. You have to try both for a while to pdecide. I’d start with an 11” because there’s better choice. Look for something used. You should find a better banjo for your money. My preference in your price range would be a Gold Tone WL-250. But get what suits you.

Welcome to BHO! Hope you enjoy your time here.

Word of warning, banjos are 2-3x as expensive as guitars of the same quality. You should understand that a $1000 is really the floor for anything that won't effectively feel like a 'toy' to you as a professional musician. Also, as a pro, you should understand that the feel and playability of an instrument is what seperated the wheat from the chaff. As a pro, I do not expect you will be satisfied with the fit/finish or playability/comfort of a Gold Tone neck. They are chunky and have a thick plasticy finish. If you are in that realm, you'd be better off getting a Deering Goodtime or a Recording King OT-26.

If I were you, I'd do whatever was needed to bump my budget up to 1500, and buy something used from the BHO classifieds. If you want a specific recommendation, my personal opinion is that Bart Reiter made the best open back banjos ever, and you should find a banjo made by him.

One other note, this is 100% a personal choice, but generally "Old Time" music is played on an 11" pot. 12" pots are more commonly seen in singer/songwriter settings. Again this is a personal choice for the musician to make. 

Upping your spending range to $1500 and buying a used model are good ideas, if possible. I second the Bart Reiter and Enoch recommendations. Also check out Zach Hoyt's banjos.
Good banjos are available with both 11" and 12" pots. For me the setup and how my hand takes to a particular neck carve are most important.
My favorite sounding open backs that I have owned have been an 11" mahogany Reiter Bacophone Plus, a 20's Vega 11" Tubaphone, and a 12" Ome mahogany Wizard. Unfortunately they are all above your current range, although you could get lucky in finding a Reiter and Wizard in the $1500 range.

Pretty good advice above. Stone banjos IMHO is the most banjo per buck. As above, there is a difference between quality and preference size of pot, inlays, tone rings, neck profile etc. Preferences come with time and experience as you glide into the music that suits your... preferences.. Bast banjered

Just peaking at the marketplace here on BHO, the 1,000 - 1,200 has a great selection right now. Folks above mentioned Stone and Hoyt, there is also a Cedar Mountain available that is also a fine choice.
 

The trend right now is definitely 12” pots. I recently had a custom build from Stone and still opted for an 11, just because I prefer how it feels. Some swear there is a distinct difference in tone but I remain skeptical. Here is one example of a comparison of the same model with different size pots Ome Tupelo 11” 12” comparison . Maybe your professional ears work better than mine! To me the difference is minimal and honestly no two banjos sound the same. Sorta like how you can have a handful of D-28s that are all different in tone to varying degrees.

All the suggestions in this thread are suitable. If I was you I would just pick whatever one looked the most aesthetically pleasing to you (since they will all sound good, perform well and retain their value well). 

The 12" vs 11" debate sort of reminds me of similar debates with bowling ball weights (14 vs 15 vs 16 lbs) and mountain bike wheels (27.5" vs 29"). Alot of the discourse for all of these (particularly so in places like reddit) is almost groupthinked into a consensus on what is perfect. When in reality, professionals use what works best for them.