Board recommendations for GPRS/GSM for 'on the go'
I have a project that have the same idea that yours.

I used Ublox NEO-6M GPS Module for GPS tracking, the module cost in a range from $6 to $13 USD(it depends from where the seller ships, china o USA) in EBAY. You can connect it via UART.

For the internet I used a SIM800L V2.0 5V Wireless GSM GPRS MODULE, you can buy it from EBAY too, it cost no more than $10.00 USD, and you can connect to internet or send SMS using AT commands.

I used a combination of arduino and Raspberry pi zero, also I send the GPS data to a webserver (I pay 5dllr/month for a VPS) and then I can track using google maps.

Thats the basic information, you can use it to start working.