For that software, one good option might currently be an i7-8700 or 8700K, which offer 6 cores and 12 threads. If you don't intend on overclocking the CPU, then the 8700 boosts to nearly the same same speeds as the 8700K, potentially making it the better value, since it typically costs not much more than $300, as opposed to close to $350 for the overclockable 8700K. At the moment, the best online pricing for the 8700 (in the US) seems to be a bit higher than usual though, with only around a $20 price difference between the two, so right now at least, the K version might also be a reasonable option even if you are not overclocking. At stock settings, it's only around a couple percent faster than the regular 8700 though.
If you're intending on overclocking an 8700K, not only would you need a K processor, but also a Z370 motherboard, which start at around $100. Otherwise, a lower-priced B360 motherboard would likely be fine. The Z370 motherboards also allow for higher speed RAM to be used though, whereas with B360 you'll be limited to DDR4-2666 speeds. Compared to DDR4-3000 or 3200, that probably won't make more than a 5% difference in CPU performance though, and less in many situations that don't depend on fast memory access. You will probably want at least 16GB of RAM, preferably in a 2x8GB kit for optimum dual-channel performance. Such a kit will currently start at around $150.
To cool these CPUs, a decent tower cooler, starting at around $30 to $40 should be good enough for stock settings. You would want something better if you decided to overclock an 8700K though, either a higher-end tower cooler or a dual-fan water cooler, which might cost closer to $100. The regular 8700 comes with a stock cooler, but it's inadequate for properly cooling the CPU enough to allow it to reliably maintain its boost clocks, so even for that processor you would probably want to replace the included cooler. A better cooler will typically be a bit quieter as well, though water coolers may add additional noise from their pump.
AMD's Ryzen processors are also a good option, and feature more cores and/or threads at a given price point. Something like the 8-core, 16-thread 2700X costs about the same amount as an i7-2700 right now, about $320, and comes with a much more capable stock cooler. The extra cores will only help if a piece of software is designed to utilize them though, and most software (including most of Adobe's) isn't optimized for a processor with so many threads. Intel's i7 processors offer a little bit more performance per core, and as a result will tend to be a little bit faster in most software that isn't able to make full use of all of the 2700X's cores. I'm not sure whether Pro Tools or other software you regularly use might be able to utilize additional cores to improve performance though.
A 6-core, 12-thread Ryzen 2600X might also be a decent option, at a significantly lower price. It has as many cores and threads as the current i7s, but again, won't be quite as fast per core. It is currently about $100 less than an i7-8700 though, and comes with a better stock cooler. For these Ryzen processors, you would probably want either an X470 motherboard, or a lower-priced B450 boards that are just starting to appear in online stores. Unlike Intel, AMD doesn't lock certain features like overclocking and faster memory speeds out of their mid-range motherboards, so B450 could be a more worthwhile option if you are looking to bring down the cost. You will probably want to go with at least DDR4-3000 RAM for Ryzen though, as it tends to perform best with faster memory. DDR4-3000 typically only costs slightly more than 2666 though.
In all, a Ryzen 2600X with its stock cooler, a B450 motherboard and 16GB of DDR4-3000 could cost not much more than $450, while with a 2700X you would likely be looking at a bit over $550 for those two extra cores. The cost of an i7-8700 build with a replacement tower cooler would likely be a bit closer to $600, and an overclocked i7-8700K build with a capable cooler might be around $700 for those components. The i7s will be a little faster than the 2600X, as well as the 2700X in most software. In heavily-threaded software, like some CPU-based video encoders and renderers, the 2700X's extra cores often allow it to pull ahead though. In games, the i7s will typically manage to get a bit higher frame rates, though with a GTX 970 at 1080p or higher, your frame rates will tend to be limited by the the graphics card most of the time in newer titles.