Cut - how much to lose and can I still make progress

Hi

5'7", 217 lbs. I am reaching the end of a very protracted NLP and in the past few months I have frankly veered into 'dirty bulking'; fast food, pizza, beer on the weekend, etc. I dont think my belly is horrible, but there's definitely a belly where there wasn't one before and it's starting to feel unhealthy. I started the NLP probably around 170, I dont know exactly. I never really weighed myself because I knew I was gaining weight and the lifts were going up. When I stepped on the scale the other day I expected 200 not 217. My pants have gone from 34-36" to now 40" waist.

My current plan is to go into a cut immediately. Any recommendation on how much to lose? I want to just pick a target and get it done in 2-3 months max. I was thinking either just come down to 200 (~15 lbs) or cut until I am back to a 35" waist and those pants start to fit, then move into a cleaner more controlled bulk. Also, is there any reasonable expectation to keep my strength in such a cut, or should I just try to hang on to what I got and expect to lose some. Current numbers are:
Squat 3x5 315
Bench 3x5 220
Press 3x5 160
Deadlift 1x5 350

Thanks.

Clean up the diet and get down to 200 lb. If you simply cut out the junk and eat less calorically dense food options you'll probably lose without even trying.