Hi Mike, welcome to the forum.
The two most popular brands are Ademco and DSC and you will find many advocates for each. I would recommend that you take a close look at the Ademco 20P and the DSC Power 832. I'm sure that either would serve you well.
You will, of course, have to add a wireless receiver to them to achieve the functionality that you mentioned. I would suggest the stand-alone receiver modules rather than the keypads with the integrated receivers.
X10 capability can be added to the DSC832 with the addition of the Escort module and it would also provide the capability of controlling not only the X10 Home Automation functions but would provide remote access to and control of the security system as well.
Assuming that your existing wiring is functional, it should work with either system but I would recommend that you replace the motions and smokes (they're due).
I sent you a Private Message with the information required to download the User manuals from the forum. Take a look at the manuals and see what features of each seem to fit your needs.
Use the forums Industry Links
page and visit the Honeywell and DSC websites and take a look at the systems.
We'll be here to help with the additional questions that you are bound to have and when you have decided on a system, we can provide you with a copy of the Installation Manual so you can get an idea of what is involved.
Don't be too intimidated by the thought of programming. Spending the requisite time with the manuals and a little help from the forum should get you through just fine.