Are you using the AT&T contacts app or the Android contacts app? They're different apps, and the AT&T app may have a smaller limit.
It has nothing to do with wifi - contacts can sync over mobile data too. Internet speed depends on the speed of the internet path from the server to you, and can drop to 0 at times (like Christmas morning) from a server you normally get 5mbps from. And if you're only getting -119dbm from your router, you're standing in the wrong place. -99 is usable, but pretty poor - the normal range is -60 to -50. (And remember that the numbers are logarithmic - a 3db change is a 2:1 ratio in signal strength, so the difference between -119 and -60 is 524288 times the signal strength.)
Install
Wi-Fi Analytics Tool and walk around to see where you get a decent signal. If the house is large, or you're 2 floors from your router (routers work horizontally, not vertically) you may need a wifi repeater. (That means finding a place with a strong signal - a number lower than -80 - at which to place the repeater, but which is close enough to where you use the phone to still get a good signal from it.)
But signal strength still has nothing to do with the number of contacts the phone can keep. (They're kept in the phone, they're
synced to the server. You don't need
any connection just to see all of them.)