It'd be far more prudent to look at the motherboard to see if it's compatible with the CPU, not the otherway around. These days, just the socket. Usually, if the sockets match up, it will work. There are a few exceptions - If you're trying to use an Ivy Bridge CPU on an H61 chipset (both socket 1155), a BIOS update could be required, and some manufacturers might not provide an update (especially on budget oriented boards). Same kinda issue with older AM3 boards - they might need BIOS updates to support the newer AM3+ CPU's, but then again, those sockets aren't the same, though some manufacturers just slap an AM3+ moniker on older AM3 boards anyway. Any AM3+ should support any AM3+ CPU without updates. I'm not sure if there were the same quirkes with socket 775 CPUs. I wasn't big on computers back in those days, but my understanding then was both the CPU and motherboard needed to support the same FSB speed, but it's entirely possible I'm mistaken on that. It could be (speculating here) that they need to match up FSB to get full speed, but if you're using an 800MHz FSB board with a 1066MHz CPU, the CPU could just run at a reduced speed (clockspeed = FSB * CPU multiplier/ratio).
There is a slight difference in performance favoring the G1620 thanks the 100MHz higher clock, but I don't think it justifies the $10 premium over the G1610. Maybe a $5 premium. The G1610[b]T[/b] is a low-power option, which will be slower, but, produce less heat and, in theory, should consume less power overall. Not that G1610 is a power hog.
BTW, the G1610 Celeron is $42 at Amazon, or $35 if you live near a Micro Center.
Yes, most NEW games would be playable at full HD (1920x1080/ 1080p) with medium settings, but something Fallout 3/NV would be playable at MAX settings. I was playing that game maxed with my 5830, and the 7770 is a bit faster than that.
If you could fork out an extra few bucks for a quad-core like an AMD Athlon II x4 645, that would be better, especially since games are starting to utilize 4 threads a lot more efficiently, almost making a requirement these days. Dual-cores aren't out yet, but if you want keep playing some new games on it for a while, best invest in a quad-core. Testing has shown a Core i3 would suffice being a hyperthreaded dual-core (2 cores/4 threads), but the AMD quad-cores are a better bang for your buck, plus that Athlon II x4 can be found for $75.
If that's a bit expensive for you, you could consider an AMD APU. The A10-5800K (~$125) has a potent integrated graphics that can game at 720p medium settings, or 1080p low settings, and features an overclockable quad-core at 3.8GHz. You would not need to buy a dedicated graphics card to game with the APU. Overall, you'd get less gaming performance compared to something like a Celeron + 7770, but a lot better bang for your buck, and save quite a bit of money since the 7770 alone can cost $120. The APU's are a very balanced package for entry level gaming.