Although not living in CR, I did break into a Holiday Inn Express last night.
Motion lights- are great, relatively cheap and usually the first place to start, get them from the home improvement store with flood bulbs or the halogen type and put them on all 4 corners of your house if viable.
Next check the locks on your doors, windows and that gate, is it cheap like your neighbors was and could they pop it open with a hammer or prybar? If so trash it and replace with a contractor grade shielded padlock. Get a welder to beef up your security gate if needed. Next look at your home during the day- the object is to make it a more difficult target than your neighbors. Do you have deadbolts, leave visible windows open? Any easy access over the fence or gates unlocked? Anything worth stealing in view from the street? I think you get the idea -think like a criminal.
Inside- find a good place to hide your valuables & cash, not in your dresser drawer or under the mattress. Look into buying a small safe and have it bolted out of sight in a cabinet or closet.
Alarms- one of the handiest cheap items I've found for outside security is called Driveway Patrol, google it. For under 30 bucks you can have a motion sensor outside that sets off an audible alarm inside, get the DC power source if available so you don't have to worry about the inside batteries going dead. The only tricky part is getting it set up and high enough so every cat, dog, squirrell etc. doesn't set it off but you do learn to distinguish if it's something small passing by or something worth grabbing the pistol for.
Home alarm- in the states you can get one installed non-monitored wired to all doors, keypad and 1-2 motion sensors for around 500 bucks, or free if you sign at least a 24 month contract. Monitored is good for some situations but not always worth the expense IMO, for instance in my town the cops now charge for showing up for false alarms. Mine's not monitored and hopefully the ear piercing alarm in the house and sirens blowing out the attic vents will convince them to leave without grabbing too much. Be sure to get the Alarm warning stickers for your windows and doors and the sign to go in the yard. I've actually just used these before with no alarm installed just to keep them guessing. Hope this helps.