Hi Terra215678
IF you are planning on directly sending 3-4,000 messages per day you will need to setup a formal link to your telco / SMS provider. A SMS modem needs about 7-10 seconds / message to connect-authenticate-send-confirm-disconnect for each message.
With a formal internet connection to the SMSC (Short Message Service Centre) you can send 100’s per second. And it is fully bi-directional, the mobiles can send SMS back to you - you just have to write code to handle / ignore incoming messages as appropriate.
These tools are costly, but generally cost less / message than direcly sending from a SMS HAT or modem.
In my previous employment I was responsible for a comms system managing an Australia wide network of technicians, and we used SMS messaging to and from the techs (this began well before mobile phones were able to handle emails and all the current messaging systems, and the SMS system is still in use today in conjunction to newer messaging as it provides a definite PUSH with notification - beep, vibrate etc - to the user).
For low volume messaging a SMS HAT or external SMS modem are entirely appropriate - see my system I built for the Commonwealth Games here
Hope this helps
Murray