First off, yes get a gravis gamepad. Simply put, there were the best gamepad for the PC for years and years. Many classic titles from the late 80's to the mid 90's take full advantage of them. They are built like a brick ***house, and will last a life time if cared for. In time Gravis phased out their classic PC gamepad and replaced it with a clone of the original Sony PlayStation Controller. It too was built just as well as the original gamepad, and had superior (in my opinion) ergonomics. The new gamepad came in both USB and classic 15pin PC game port variants. Both versions have a little brass screw hole in the middle of the d-pad that was made for a little plastic stick to screw into it and make it feel like a mini joystick. These little plastic sticks are kinda rare nowdays as they did not come with the game pads and had to be ordered by the customer. Between the trouble of ordering them and the price with shipping, very few people did this. Its nothing great, but if you can find one at a reasonable price, then by all means get it. I happen to like mine. Either way, both Gravis gamepads are well worth getting and you will not regret it.
Second part is pretty much a no. Yes, there were a few projects out there that would work with Wondows 3.11, but not Windows 3.0. As for the browsers that you can get working under 3.11, I have no idea how to get them working on a modem connected rig. Virtually all ISP's that still let you dial in, will pretty much expect a 32bit TCP/IP network stack that you simply cant get under 3.11. There were a few proprietary browsers with proprietary network stacks that worked with 3.11, but they were for ISP's that have LONG since gone out of business.
You may be able to get Lynx or some old Contiki project working, but its really not worth it. Also getting modern pages to load on a dialup from a Windows 3.0 era rig would really suck. My guess is the modem would be 28k bps or 14.4 if you were lucky. Heaven forbid it turns out to be a 2400 or even a 1200 bps modem. Just getting Google to load could take a minute or two and that's about as simple as a page gets now days. If you really want to see the web on pre '95 versions of Windows, then here is what I suggest.
Upgrade your version of Windows to 3.11. Get a null modem serial cable, and hook it up to a modern PC (you may need to get a USB to serial adapter to do this if you don't have a serial port on your modern PC). Establish a serial connection between the two and make sure that the modern PC is online of course. There are lots of pages out there that will teach you how to do this. Once you've taken care of all that, then start up something like Lynx or some have baked browser from that era and enjoy the web. I just don't see that's its remotely worth the effort. But there is a few other com options for you. Start looking for BBS's that are not only still up and running, but still taking dialup connections. Load and run some class BBS software (either in DOS or Windows as there were a lot of them for both platforms), and enjoy. You can also tunnel through your modern computer via a serial connection and use telnet on that old beastie.