I am planning on purchasing a dell optiplex 790 for an emulation build and was wondering if an i5 2400 and 8gb 1600 ddr3 ram with my spare radeon hd 7770 will be enough to play the following games at 1080p 60fps on dolphin's latest stable build.
Just Dance 4
Wii Sports Resort
Mario Kart Wii
Super Smash Bros
Be aware that Dolphin's latest stable build is 5.0 from over 7 years ago, but since then Dolphin seemingly transitioned to a rolling-release model with it's "beta" versions and therefore stable builds basically don't even seem to be a thing anymore.
Regardless, a key problem is that there are two variants of the Dell Optiplex 790, and
one of the two variants can only support half-height GPUs (commonly called "low profile"). This is key because the HD 7770 was only ever available as a full-height GPU and therefore won't fit in the half-height version of the Dell Optiplex 790.
That being said, I'm going to go out on a limb and suggest that, while the games you're looking to run are not at all demanding and might be fine on an i5-2400 (don't quote me on this...), there's actually a decent chance of being CPU-limited if paired with an HD 7770 (assuming that even matters in the context of the GPU fitting the PC and/or the games don't just run at 60fps on an i5-2400 anyway).
The thing is, unless you're for some reason getting an absolute amazing steal-of-a-deal, emulation workloads is one of the rare few cases where an Intel Core 4th gen "Haswell" CPU (or newer of course) would net you like a 30-40% performance upload per-GHz. While these "Haswell" CPUs are 2 years newer and therefore possibly more expensive, they're still
11 years old by now and therefore surely can't exactly cost much (if any?) more of a premium.