SMSD natively supports MySQL and PostgreSQL. However it has also support for libdbi, which provides access to wide range of database engines (eg. SQLite, MS SQL Server, Sybase, Firebird,...). Unfortunately libdbi currently does not work natively on Microsoft Windows, so you can use it only on Unix platforms.
Since version 1.29.92, SMSD can also connect to any ODBC data source, so you should be able to connect to virtually any database engine using this standard.
Yes. You can use some of example interfaces distributed with gammu in contrib directory. Or there is full featured separate interface written in PHP called Kalkun.
Standard phones usually do not perform good when used long term as a modem. So it’s always better to choose some GSM (GPRS, EDGE, UMTS) terminals/modems, which are designed to be used long for term in connection with computer.
The best option seem to be Siemens modems (eg. ES75/MC35i/MC55i). Slightly cheaper, while still good are modems made by Huawei (eg. E160/E220/E1750/...). We have heard also positive experiences with cheap modems from various Chinese resellers like DealExtreme or Alibaba.
You can check other user experiences in Gammu Phones Database.