Oh yes. That is my aspiration – to get to the point where I have my own simple home gym, and no longer have to pay for a crowded and stupid commercial one…

10 planks, 30 seconds each. Not 10 sets of 10.

10 sets of 10 planks (30 seconds a pop)?

All workout programmes depend on two things – progressive overload, and consistency. The first simply means you start small and work upwards. The second means you show up every damn day and work out.

The key thing to remember is, the body is a chain of muscles and nerves – so your workouts have to build strength across the whole body. Push-ups and chin-ups are compound exercises that use lots of muscle groups. So, you have to strengthen them together.

For push-ups, start by doing push-ups on your knees – 10 at a time, building up to 10 sets of 10. Then work on doing planks for 30 seconds – 10 sets. Work up to a minute for the planks. This will strengthen your arms, core, and back.

For chin-ups, start by doing a hang to build up your grip strength with your feet on the floor. Once you can do a full minute, move to hanging with your feet off the floor completely, for a full minute. Then start using resistance bands to assist you in doing your chin-ups, of steadily diminishing tension. Eventually, start going to one chin-up (or pull-up, they are the same exercise but with different grips). Then work up to 5. Over time, you should be able to do 10 or more in rapid succession.

In my own case, I went from never being able to do a chin-up as a kid, to banging out 20 – all the way up, all the way down – as a finisher at the gym on bench days. And I’ve been able to do that sort of thing for over 15 years. It’s all just about showing up and doing the work – literally nothing more.

Like furor said, push-up pivoting at the knees and not the toes. You can also start with an incline (ex. a chair) so you don’t do full-range right away. You will progress fast.

As for chin-ups, if you have access to a gym they have machines that do assisted pull-ups. Or you could use the lat pull-down machine, and build up until you’re close to your body weight. If you can’t do a gym, get one of those weighted elastic straps and mount it above your head, and pull down on it. You will progress fast.

pushups can be done from the knees instead of the toes. and i suppose if you’re really bad off, you could just bend at the waist.
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to work into a chinup, i would find a kiddie/women’s bar that you can just barely chin while standing and then do leg assisted as needed. try to finish up the leg assists with one long pull without the legs.
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i will say that the fastest i ever lost weight i would walk a 1/4mi and do chinups, then jog a 1/4mi and chinups, repeat until completing a mile. i stripped off 30lbs in two weeks without even trying. i wasn’t even weighing myself until the end of the 2nd week when my pants were falling off.

Thankfully, I’ve noticed that the January rush usually only lasts 3 weeks, so it should end soon. This is actually a good time to rest and take a break if you need it.