Don't even start by buying new home gym equipment. Go to facebook marketplace and look for any adjustable gym bench (~$50) and adjustable dumbbells (~$100-$200 depending on how much weight they can hold). What's that? You don't know where to start?
My recommendation is to start low volume, moderate to high intensity. Two to three sets MAX of 8-10 repetitions. If you go through a full set of 8-10 feeling like you’re out of gas then you’re using too much weight. Drop it down to where a full set makes you feel like you can rest up for at least one more. Between each set you should be resting 2-5 minutes (or however long it takes you) until you feel like your heartrate has dropped and your muscles feel ready to start again. At the last set, it should feel like you’re close to or at failure. Unless you just want to do all of these in a single day, take your time, you're a busy person! Start slow and split these into three days a week broken into Tricep/Shoulders/Biceps; Chest/Back; and Legs. This will probably take about 30-45 minutes a day.
Triceps
Overhead dumbbell tricep extension
Dumbbell skull crushers
Shoulders
Dumbbell overhead press
Front, side, & rear delts
To target your front delts, hold the dumbbells with a neutral grip and lift them straight in front of you. For side delts, raise the dumbbells out to the sides at a slight diagonal. To hit your rear delts, use a pronated grip, lean your torso forward, and lift the weights out to the sides in a reverse fly motion.
Biceps
Standing bicep curl variations
If you use a supinated grip to perform bicep curls, you'll primarily work your biceps. If you use a neutral grip, you'll shift the emphasis to the brachialis and brachioradialis; you'll still be working your biceps but to a lesser extent. If you use a pronated grip, you'll shift even more workload to the brachioradialis and even less workload to the biceps.
Chest
Flat dumb bell chest press
Inclined dumb bell chest press
Dumb bell flys
Back
Dumb bell back variations
If you stand upright and shrug your shoulders while holding the dumbbells, you'll target the upper traps. If you lean forward and perform dumbbell shrugs, you'll work more of the middle traps (while upper traps still engaged). If you lean further forward, keep your elbows slightly bent, and perform straight arm dumbbell rows, you'll primarily work the lats. If you hold the dumbbells in front of you with a pronted grip (palms facing back) and perform dumbbell deadlifts while keeping your back straight, you'll be working the lower back as well as the glutes and hamstrings.
Legs
Quads
Bulgarian split squat
Goblet squats
Glutes
Forward lean squat
Forward lean Bulgarian split squat
Inner thigh & hamstrings
Wide squat
Stiff-leg deadlifts
more
