You're looking for a system similar to mine, you would need the following components for what you are trying to achieve:
I shall be using TPE instead of repeatedly putting "Texecom Premier Elite".
TPE 48 Control Panel (you could buy the 24, but I pick the 48 as it allows for expansion, as well as coming in a metal case instead of a plastic one).
TPE LCDP Proximity Remote Control Keypad (this keypad supports RFID fobs for arming/disarming the system, you could purchase a simpler, cheaper control panel such as the TPE Standard LCD Remote Keypad, or the TPE LCDL Large Screen Remote Keypad).
TPE 8XP Remote Zone Expander (you can hold off on this, this is what turns the system into what is called a "hybrid system", a system which uses both wired and wireless. You will only need this component when you decide to install your additional wireless PIR. This particular unit supports up to 8 devices, if you think you would ever need more than that, please look at the TPE 32XP-W Ricochet Wireless Expander, this allows up to 32 wireless devices).
Finally for the remote arming and disarming of the system you will need the Texecom Connect SmartCom Ethernet and Wifi Communicator. As the name states this can be connected using either ethernet or WiFi (obviously ethernet is the better choice if you can run the cable).
You may also wish to purchase the Texecom USB-COM Interface Connector. It is a little pricy for what it is, but speaking from personal experience, it makes setting up the new system 10 times easier than trying to do it all from the panel. This wire would allow you to connect the alarm to your computer and then complete all the configuration using Texecom's "Wintex" software (I think you have to register on Texecom's website as an alarm installer to access it, but there is no "vetting process" so anyone can do it).
Bare in mind that the sensors could use an older style of wiring not supported by the new panel. Without further information it is hard to advise you. However if you could get a picture of the inside of the current box and post it, it may go a long way to helping us to assist you.
I'd also be happy to provide any help you need in configuration of any new systems.
Good luck!