My wireless router is in my study upstairs, and covers the whole house and garden with no trouble. My neighbour the far side from where the wireless box sits can't quite connect to my network, but he's four brick walls and 50 yards away. It's very much down to quality of the WiFi device, and antenna placement.
My "other" hobby (amateur radio) taught me the vagaries of antennas and how they behave. Just putting on a longer piece of wire won't cut it: the antenna needs to be resonant. You can do clever things with extension antennas, but then you can do it easier with a LAN cable to a remote WiFi unit.
My tips would be:
1. Avoid Belkin - I've never had any success with anything of theirs.
2. Get a WiFi with two antennas - that's diversity operation. Results are likely to be far better than with a single antenna.
3. Make sure the WiFi manufacturer sells a suitable "repeater", in case you find you need one. Mixing brands of repeaters isn't a game for the faint-hearted.
4. If you need a repeater: they are pretty simple to use - get the network running satisfactorily first, then add the repeater, located where there's still a good signal from the primary, but in the direction where you have problems.