I would suggest buy an UMIK-1 and try REW first, its cheap (around $100) and the mic is usable if you decide to use more advanced room corrections like Dirac in the future, or want to do measurements and send to Thierry (https://www.homeaudiofidelity.com/)
And while, in some cases, time/phase corrections can give a little extra, its very limited what you actually can correct for time/phase in a typical stereo setup. In most cases, the biggest benefit of digital room corrections is correction of frequency response in 20 - 200 Hz.
Feel free to have a look at my guide as a start: A guide how to do room correction and use it in Roon