Do not get motherboard with 970 Chipset for FX 9000 series, they might struggle even with FX 8000 series, plus on the other hand, no 970 chipset motherboard can't support FX 9370.
The cheapest 990 chipset motherboards that support FX9370 are the Asus M5A99X PRO R.2.0. and the Gigabyte 990FX-UD3. REV. 4.0., both of them are in the range of $120-$140.
Btw here are some benchmarks
Here you can see that at stock speed the FX 9370 and overclocked FX8350 to 4.4 has the same score as stock FX9370
CPU Mark 9,846 for FX 9370 at 4.4
CPU Mark 9,875 for FX 8350 at 4.4
http://www.passmark.com/baselines/V8/display.php?id=21720823677
http://www.passmark.com/baselines/V8/display.php?id=21747421394
That 30 points difference will make no performance difference at all, and even if it was 100 or 200 points difference. You will have to be a robot to spot the difference in real life scenarios.