I can start to see the limitations in Audacity. If you could have any of the paid DAWs in the 100 dollar range or Pro Tools free and you were recording less than 16 tracks with minimal effects and no vocals…what DAW would you get? Does PT free offer enough for that?
What about the PreSonus offering? For use with a Mac i7 8 gigs ram.
I’m a Windows guy and I don’t have enough experience with different DAWs to make a recommendation…
REAPER is $60 for home & small business use. (There is a “pro” license if you’re making more than $20K a year using it, but it’s the same software.) REAPER known for being powerful and flexible but it doesn’t come with any virtual instruments (probably not important if you’re currently using Audacity) and some of commercial plug-ins don’t officially support REAPER (probably because most users don’t want to pay more for plug-ins than for the DAW).
I haven’t heard anything good about the free version of Pro Tools. 
I have read good things about Studio One and I think it integrates with the Presonus digital mixers (for motorized fader automation, etc.). But, there’s more than one version and the reviews/reports I’ve read are probably for the most expensive version.
Cakewalk is now free, but unfortunately it only runs on Windows.
I’d use Audacity.
I mostly only use other DAWs when I’m wanting to apply a lot of effects, and want to be able to adjust them on the fly.
If money was an important consideration, I wouldn’t use a Mac. Apple charge a big premium for their name, which could pay for a commercial DAW program and a nice sound card.
If I really had to use a DAW on a Mac, I’d use Logic Pro, but that’s a bit over your quoted budget.