I was thinking about upgrading my GPU. My CPU is the Intel i5 4440S @ 2.8Ghz and was wondering if the NVIDIA Geforce GTX 660 ti would be a good match for the CPU as in, one of the two wont bottleneck each other?
Yep, it'll work fine with your CPU. The 4440s is a decent processor. It should be plenty good enough for any single card gaming system. Just make sure your case is large enough and your PSU is powerful enough and you should be good to go.
my case Dimensions are 173 x 360 x 400 mm (WxHxD)
242 x 480 x 513 mm (WxHxD) with Carton. Is that big enough? and my power supply is only 300 watt, which is weak, will any power supply go into any tower, or only specific ones can?
Your case should be good. A stock gtx760 is 9.5 inches long so you'll need that much space by the pcie slot. You will need a new PSU and any regular one should fit. Make sure to get a quality one as well. I'd recommend a good 550-600w one as it'll leave you plenty of room to upgrade/add other components over time. If you don't plan on doing anything else a decent 500w will do as well.