Your chances of success depend on what you want to do with it.
You can buy a new external modem from $50 to $100+ US.
The nice thing about an external modem is that you can easily use it on a new computer if you upgrade.
You could also pick up an ISA internal hardware modem, 28.8 or 33.6. You can find these on EBAY usually under $20. Better than that would be to find a local computer store with used parts and pick up the stuff there.
Whatever you do-DON'T buy a WINMODEM for your Windows 3.1 system. These are made specifically for MS Win 95 and up and generally don't last long.
A new CD-ROM drive will cost you $40 and up. This is also something you could stick in a new system if you upgrade.
In 2 of my 486 computers I have old 2X CD-ROMs. Both are proprietary types which require a soundcard/interface card to operate. I bought them both on Ebay. Since I don't play games much, I don't need anything faster. A 2X is fine for installing programs and listening to music.
If you are just starting out messing around with computers, you are better off looking for an IDE/ATAPI CD-ROM. This is the type that can just be hooked up as a slave to your Hard drive. They are simpler to install than the proprietary type.
As far as the Internet, I use a 486 fairly often since my daughter seems to have taken over my computer.
You should also get a soundcard, which you can figure on spending $15 to $30 US for a 16 bit cheapo.
Good luck