I once lived in a very shady part of Glasgow, and my flat had an alarm. I didn't feel I needed an alarm, but it was very handy, in particular the door chime was very reassuring - it chimed every time the door opened. The alarm itself was a nuisance, it drove my neighbours mad by going off all the time.
If you are mostly worried about people entering, I'd get yourself some loud door chimes on all external doors, and get some motion sensor outdoor lights.
Overall, not sure exactly where you are, but London is quite safe nowadays; as you said it's petty crime like thefts you need to prepare against; these sort of criminals are after easy money only. Depending on how you present yourself, criminals, like lots of the population will make assumptions about how much money you have by how you dress and what you flaunt. If you have a top of the range car parked outside, loads of boxes in the recycling for consumer toys, and are seen with bling you could be a high value target. I often think if a burglar comes to my house, they'll see my car (in serious banger territory, paint is flaking off), my home decor is very functional etc, and there is nothing worth stealing....no TV, bottom of the range laptop, cheap phone...I'm pretty sure the burglar will believe me when I say I don't have any cash, and I can offer my purse which usually has less than a tenner to them.
It might work to prepare yourself for the worst; even if the unthinkable happens and you get burgled, you will get through it. Sure you'll feel horrendously violated, and the bureaucracy of dealing with the police will grate, but you are strong enough to get over it - they will only take physical objects, which can all be replaced.
But do what makes you feel better and sleep at night, get an alarm, chimes, cameras, lights etc.