That's horrible! You have my sympathy. Such a damn nuisance. The best way to make the garage personnel access door secure is with a conventional doorlock like a house - the kind you pull up to activate the lock then use a key to lock it fully. Then that door is as secure as your house.
If your garage has a window, get some anti-smash film put on the glass - it's not expensive and you can't see it.
For the roller shutter, a huge padlock that is almost circular (not a loop shank which can be reached with bolt cutters but where most of the shank is covered by the body of the padlock) is the best method, fastened into a special pin which is in turn concreted into the ground; that too will deter thieves. If your garage is harder to break into that others, well ... they'll go for the others.
Sorry the description of the padlock is so inarticulate. We got in a security company to sort all this out for us and I don't have the name of the lock style or brand, sorry.
We did have a monitored alarm on the house and the garage as well (this was when we lived abroad, in a country with a high crime rate, can you tell?) but honestly it was a PITA. False alarms drive neighbours mad, if you want it monitored it is expensive and you have to provide key holders etc etc. A real hassle. When we moved here we expected to have to install all that stuff again and were pleasantly surprised when it wasn't needed, good locks and good lighting did the trick.
Good luck with re-securing. If you let your insurance company know about the upgraded security measures you've taken, they might not be quite so horrid about increasing your premium next time around (because it will surely increase, alas).