There should be 2 of those coax connectors on back... one for cable tv/antenna and one for FM...
If you have cable, route the cable to the cable tv connector and you can use the included antenna cable to connect to the FM connector. Or, if you don't have cable, you can should be able to use the included FM antenna to connect to the cable tv connector. I don't remember if it requires turning a bolt to secure or if you can simply push onto the cable tv connector, but it definitely should fit.
regarding the integrated web browser, I never tried so I can't help there, but someone else maybe can pitch in here?
is this still THE tuner to buy?
depends what you need. if you want to do other stuff while recording (like play a game or something) then you may want to consider a hardware encoder tv tuner card instead. if you want a little better recording quality, you might want to consider the EXPERT version of this card rather than the Deluxe.
As far as how this card compares with other brands with the same bt878* chip, while I haven't tried all of the ones out there, I would say this one is better than the Hauppauge WinTV 401 for sure (better remote and more polished software with more features), and likely better than the rest of the competition in its class overall.
I liked the ComPro tv tuner card, but it uses a Philips chip which isn't very well supported by 3rd party programs, so that's no good...
If you want better quality viewing, low CPU utilization, and maybe better quality recording, I would look into getting a Hauppauge PVR250-MCE (amity or roslyn), Leadtek PVR2000 (based on blackbird design), or AverMedia M150 (based on blackbird design), IF you can get one for a reasonable price. Personally I'd wait until I spot a deal for $69 shipped like there was not long ago in the hot deals forum before the prices got jacked up due to the AT/FW effect. But if you're in a hurry, the last two of the 3 cards mentioned above can be had right now for $75 shipped (just do a froogle or pricewatch search.)
Just keep in mind that the roslyn/blackbird-based designed cards are newer and not fully supported yet, but support has been improving and is going to come since these are the next generation cards. They're already supported by BeyondTV and SageTV, but if you want the widest support at this time, you'll want an amity-based card like the older PVR250-MCE cards or a retail version PVR250, but they're going to be more expensive by another $25 or so. So it's not really worth it in my opinion to get the older ones.
In any case, these hardware encoder cards are a good $30-$55 extra over a Leadtek Deluxe, so you will want to think about what you want the card to do. If you just want to watch TV, record in pretty good quality (but not the best you can get), and don't mind not doing too intensive multitasking while recording tv programs, then save the $30 and get a Leadtek Deluxe. If you want a little better quality recording, get the EXPERT. If you want lower CPU utilization so you can play games or something else and want higher quality tv viewing (and possibly higher quality recording quality as well), then get one of the hardware encoder cards.
Hope this helps..