Sean Lerwill's books & programmes are good, incorporated them into my normal gym sessions & routine. Complete Commando is also a good week by week progressive plan, it's worked wonders with my running so would definitely recommend. I would also say get yourself on a mobility workout too, improve your fitness alongside your recovery and such. Complete Movement from the same as CC above, 6 15 minute sessions a week focusing on stretching & mobility, it sounds like a corny review but have never felt better.
If you don't want to pay for anything, there are several good training plans here & on the Royal Navy's website.
I was like you with regards to starting from scratch. At the start of lockdown 1.0, I was 105kg, in my final year of uni & couldn't run the mile and half, let alone the press ups etc. Now, almost a year on, I'm running 8-9 minute miles, able to complete 3 full rounds of the vpjft & a fourth with a break in the press ups. I', sure you'll get there, just got to find that direction to start with.
Welcome. Hopefully others here better qualified than I will chip in with their suggestions
Body weight loss and a regular running regime will be a good start. A calorie deficit diet aiming for a consistent 1.0 kg per week loss is generally considered sustainable. It doesn't sound like much but the weeks will fly past.
At first, running might seem like hard work but start gently and stick with it. Once some body weight has been lost and the body has adjusted to exercise it will become easier and improvements more noiceable as you are able to ramp up intensity.
Adding appropriate core strength and mobility stretching exercises should help to fend off too many niggles and injuries.