If you want a CPU for $125 range that can supply good on-board integrated graphics, I'd recommend actually going with AMD on this one.
AMD A10-5800K is a APU - which is a CPU and a GPU combined. This has a really good on-board GPU opposed to anything released by intel.
Link:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819113360
But - you'll need a Socket FM2+ motherboard for this, so if you don't have money for that I can recommend a Intel CPU for your motherboard socket
Intel:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116945
It's a bit more pricey, but the Intel HD 4600 is a pretty decent on-board GPU and it caches 256MB of your RAM, and it can be used for light gaming and most definitely web browsing. With the LGA1150 socket (same with the 4130 you were considering) you can upgrade to an i5-4670 or even a i7-4770 in the future seeing as they share the same socket.
I'd recommend going with Haswell for any Intel CPU - they're reliable and are really power efficient, they tend to run a bit hotter though so I'd recommend you get a aftermarket CPU cooler even if you're not overclocking - but seeing as you're just going to web surf I guess you won't have much of a problem with overheating.