Home gym. What do I need?

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Hi all, a couple of months ago I left my job which had an onsite gym which I took advantage of 5 days a week. I was doing the 5x5 plan (if I could get on the bench and rack).

So I''m now in the situation where I need to get some things for a home gym. I'm only doing press ups at the moment.

So what should I get do you think? I need a bar clearly, but what size? Olympic or 1"plates? I do have some 1"plates actually, so if I could get away with a narrow bar then that would be good. I need a bench I guess? Do I need bench press stands or a proper rack?

Ido enough running and cycling for my cardio I think, but don't want to get skinny fat.

Thanks all.