Good luck Berukie. The hardest thing is getting started, once you do, the questions will answer themselves. Make sure your glutes, quads, hamstrings and any tendons cut in surgery are as strong as they can be. I initially had some adductor weakness and held off from running until I could complete sets of single leg glute bridges on the affected side. Also, fairly obviously, make sure you have rebuilt enough aerobic strength. Although I was able to continue swimming right up to surgery, and got back in the pool 5 weeks after surgery, I was quite surprised how much capacity I lost during the period before / after surgery when I couldn’t run.
I have stuck with the shoes I had before surgery, both were fairly new when my running started to fall apart in early 2021. Fairly normal Mizuno Wave road shoes and Saucony Guide trails. Not sure where you live and therefore what options you have. Trail might make an easier start so long as you have somewhere with a good compacted surface – wide and well maintained paths, not riddled with roots, not a lot of mud etc. treadmill likewise if you can bear it (I would rather be outdoors!).
I am now just over 4 months out from my THR and made a tentative start to running in December, which I am now building on. I started with weeks 1 and 2 from couch to 5k as I hadn’t been able to run since May, and am now using coach Amy’s 5k plan on Garmin Connect to build on it. Basically run/walk until I can continuously run 5k. I am a big fan of parkrun, currently walking it as fast as I can with Nordic urban poles, I won’t switch to running it until I have got through (or close to through) the Garmin plan.
I have an excellent personal trainer who I have worked with on strength for a number of years. He has been excellent in getting me into some sort of state to tackle this. Plus as I mentioned I swim and I also do pool based Aqua classes.
I am not sure whether I will go much beyond 5k. I probably will build back to 10k but that’s enough. I am 65, main motivation for running is the physical and mental health benefits. Nothing seems to help in quite the same way.
I have a Smith & Nephew uncemented Polar 3 (Polarstem / R3 cup), surgery was posterior approach. My recovery has been really easy and straightforward.