Protecting the spine is all about bracing and posture in everything you do. You can lift weights if you take the time to develop those postural habits, like an arched spine and iron tension in the squat and deadlift, and not kinking your back in the overhead press. It's easy to lose discipline and try to lift more than you can brace. Read a few books on lifting technique. Watch videos by reputable guys like Allan Thrall.
I recommend starting calisthenics before you try Muay Thai. Calisthenics make things easier. You can start at any time, anywhere, and everybody should be able to knock out a decent number of push ups, squats, step ups, back extensions, inverted rows and pull ups. Everybody should know how to run, jump, crawl, climb and swim.
Sit ups are not necessary and not recommended if you have spinal problems. Other exercises work as well for the same thing.
Most of all, get your diet right. If you want 20lbs of muscle added to your frame, you have to eat like guys 20lbs heavier who work out. Get some stews going a few times a week and learn how to cook 4-8 meals that you love.
Dieting and training principles are the same whether the resistance is a push up or a bench press, although over time, you should master both your body weight and a barbell.