A lot of this depends on what infrastructure your client already has in place, what level of risk vs level of spend you and the client are willing to undertake, and how important the availability of these web apps are to the client's business.
Be that as it may, in order to have your web app available to the outside world, fronting for the client's MS/Dbase backend (presumably totally private), you'll need at a minimum:
- A link to the public Internet - yes, this should include a public IP (or a set), provided by most ISPs
- A router, between the client LAN and the public Internet - again often provided by the ISP
- A firewall: this can be done on the router, or on an additional box
- router: pro: will most likely be bundled with the line cost, con: routers (even with GUIs) are difficult to maintain in a dynamic environment and aren't as flexible as OS-based firewalls;
- box: pro: your choice of firewalling environment, including many additional features, con: costs in both money and time
My quick 2c regarding firewalls (as the link, router, IPs is something you'll have to do the research on around ISPs in your area):
If the customer is willing to pay, and would like to manage this themselves one day, since they already have MS infrastructure, I'd recommend Microsoft's Security Server offering - this may even be possible to run on the same MS box, so only licensing would be the cost.
If you're willing to learn and the customer doesn't want to spend anything at all other than link costs, then when doing your research see what routers/interfaces to managing your link the ISP provides and whether it offers the correct security for your purposes.
If you're willing to learn and the customer is willing to spend a bit, then a *nix-based firewall distro on a 1U box is a great way to go. There are many firewall distros to choose from (far be it for me to recommend to someone who wants to learn ;) ), and you will learn a lot, guaranteed.
In closing, in my mind based on the tone of your question (and without prior knowledge of your background and experience), I'd suggest at least a passing knowledge of the following to start you on your road to network infrastructure builder:
As usual, HTH && YMMV.