Some "mid level" tracons are highly seasonal and can be every bit as difficult as the large tracons. Not sure about BNA per se, but do your research for sure. A facility's level is not always indicative of the performance level required.
Lower level radar facilities will teach you the basics. You’ll probably get exposure to the different challenges of radar; such as airspace boundaries, aircraft performance characteristics, vectoring to the center environment, vectoring to an airport, speed control, divergence etc.
having said that, be prepared to apply all that information you pick up at a much faster speed when you get to the ‘big shows’. My suggestion would be to get comfortable with the scenarios you’re presented once you’re certified.
A lot of people at smaller tracons, who aspire to get to the large facilities, get way too worked up trying to master things they think are important at bigger tracons.
the bottom line is, you can only determine if somebody has the aptitude to work at a busy tracon once they get there and start training. But having a solid radar background will accelerate your progress.
the long winded answer to your question is: yes, an 8 or 9 would be a great place to start