This question brought back some memories. I started playing with alarms when I was about 5 years old, started with disassembling a Yellow AND Black Bike Siren that made Police, Ambulance and fire sounds(Anyone remember these?). Being a bit of a hoarder, I still have bits of it. If you are new to electronics, then 555 timers are a great starting point. 556 is a dual version. Also LMC555 and TS555 are CMOS low power versions, so you can use batteries and they will last ages, if you get the circuit right.
Your other friend in discrete logic is the HEX Schmitt Trigger CD40106B. You can make timers, clocks, latches, sirens and lots more with these.
However, In today's world, you really need to be looking at uC like Atmel & PICs. You can buy an Arduino Micro Pro with a ATmega32U4 for under £5 and has enough processing power to sink a small battleship. At the DIY level, you would need very few parts to build a good alarm system, you can add a £3 ESP8266 to it, and you would have a Wifi enabled system.(But you will need to get good at coding and that's a good skill to have.) On a professional level, alarm systems have a little more to their design than just logic.
Most alarms today, used ADC's on there I/O and measure the circuit resistance to be able to detect Tamper, Alarm and Faults. Also components like EMI Filters, ESD and Surge Suppressors. Watchdog and Current Monitoring. On top of this is a whole load of Firmware, Software and Testing. Hope this helps.