WeybridgeBill
Lurker
Hello
I
I
Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
The fact that it will need to " b) dial numbers and/or send text messages dependant on certain criteria" means that it will not run on any iphone since this is not a supported API. As far as I can tell any android phone should be able to do what you said, including the first Android phone, the T-Mobile G1/HTC Dream.
Cheaper Android phones are generally of poorer build quality and slower hardware. Other than that, the entry level models from trusted vendors like HTC, Samsung etc are still perfectly usable. I would avoid buying some cheap thing from a Chinese web store, they're cheap knock offs and give Android a bad name.
Pick one with Android 2.1 if you can help it, earlier versions can't use all of the apps on the market. Plus it's good to be up to date with the OS.