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I'll leave the programming to others, but your bodyweight is not keeping you from your goals as stated.
I'm 5'11", >350lbs @ >40% bf. Squat and dead around 550, benching about 300, and overhead about 240. Expecting these all to be considerably higher (specifically deadlifting) before summer's over.
Unless you have a serious health concern about that extra bodyfat, just lift and stop overthinking - I used to do the same thing. Granted, my bodyfat is in actually dangerous levels but yours isn't. Just lift. Recomp later when you have more muscle mass and you're stuck in week or month-long periodization cycles.
There's a whole lot of other considerations to be made that aren't apparent in your question:
How much other activity are you doing (i.e. cardio) that may be impacting your recovery already?
Are you sleeping regularly? How many hours each day?
What is your diet like? What are the exact macro numbers you're consuming?
You have a lot of lean body mass, there's no way (in my opinion) you're close enough to your strength potential that you'd need to lose what little extra weight you have.
Conditioning work will impact your recovery until you're acclimated to it. Start with doing it once a week for three weeks, then maybe increase to twice a week. Not more than that. You'll get better weight loss, if that's super important to you, managing your diet closely than trying to add a bunch of conditioning.