If you could only choose one leg exercise ..

[Nailest]

to do, with no equipment, at home, and that gave good results, what would you choose?

Squats, done with proper form

Done properly, squats are also good for your core: you need to brace your core to do them properly

And other all-body exercises:
Burpees - full chest to floor
body weight push ups, with proper form

I can’t do the curtesy ones or the one legged ones, my balance is terrible.

Then that's what you should work on - it's probably that your core is weak. Balance comes from braced abdominals.

Also for balance make sure in your lunges that your legs stay in line with your hips. I'm dance-trained and tended to do lunges with feet in a straight line so my legs almost crossed my body centre line. Once I kept my legs a hip-width apart, my balance was better.

Also, think about dropping your pelvis straight down, rather than bending your legs.

Thanks for the explanation @HundredMilesAnHour.

And thanks also @GoodThinkingMax for the advice. My core is undeniably weak (as is the rest of me!) Trying to address the issues now :)