I would check out some used banjos. Unless they are really nice Open backs are usually reasonably priced. Elderly usually has some, depending on where you live it might not be easy to find them, but to my ears if you want to play old time music, an old banjo sounds much better than a cheap new banjo for the same money. It might be a no-name or a banjo put together from pieces of good older banjos. If you have enough money to buy a Reiter you can probably find a really nice older banjo for the same money. Although the Reiter is nice. Many years ago I bought a handmade 1880s vintage Banjo from elderly for very little money and it has ended up being a great friend. (They don't sell them cheap anymore I believe).

If you buy a cheap banjo it is not going to matter if it is fiberskyn or plastic there will not be that much difference in tone. I have a very old junky tenor banjo with a very thick calfskin head...it still sounds cool.