For games the drive speed does not particularly matter, just about any drive will do... as long as you have enough drive space in the first place. If you want really fast load times, then get a SSD or SSHD, but otherwise all HDDs are going to be in the same ball park of performance.
Light photo editing also does not matter as the photo will likely be loaded into RAM which is insanely fast compared to a drive, and it only reads and writes when initially opening the file, or saving the file. Just like games, as long as you have enough space you are good.
For editing 4K video... there you are talking about pretty hefty performance (and reliability) demand, especially if editing multiple 4K streams at once (like with a fade or effect). Either the video is highly compressed consumer footage, in which case a consumer drive is plenty, but it is going to be really rough on your CPU... or you are going to have uncompressed (or lightly compressed) pro footage and you are going to want something like a RAID1 or 6 (raid 5 has issues) array in order to feed footage fast enough and reliably enough to be consistent.
At any rate, if you are looking to save money, then work with what you have first. If you have a perfectly working drive, then throw it in there. You can always reinstall, or reimage to a newer/larger drive later down the road. Nothing says that the drive you start with is the drive you will end up with... I have gone from a 1TB 7200.9, to a 3TB 7200.13, to 2 240GB OCZ agility 3 in RAID0, currently 2 256GB Plextor drives in RAID0, and in another year or two I will no doubt move up to a 1TB SATA express drive when I rebuild my core system. Work with what you have, and upgrade when you can.
As for Seagate vs WD, I know that some have some very strong opinions on the matter... but it really depends. If you have the money to spend I can tell you for sure that WD has better customer service and it is much easier to deal with when there is a problem, but you pay a premium for that service. Seagate is really hit-or-miss. I am a person on a budget, so pretty much all of the drives I put in my own systems have been Seagate, and over the last 2 years I have bought 8 3TB drives for use in NAS setups for a friend and I, and we have only encountered 2 bad drives. They were both DOA, so it was a simple matter of dealing with Newegg and Amazon to get replacements. But at the same time I am building a small server for a nonprofit that does a lot of video storage/editing, and for them I would never purchase a Seagate, and am planning on picking up 4-6TB WD Red drives for the sake of the warranty and customer service.
The difference is that my home server has plenty of redundancy, and even if everything dies then it is merely an annoying process of re-ripping all of my movies to the server. If the business has their server blows up then it means loosing years of video footage that they cannot get back (because their tapes are degrading), and I will not be there to monitor it every day or two to catch issues as they happen, so I want something more reliable.
The other thing to consider with WD is that their drives are sort of a pain to work with, especially when it comes to more complicated setups. With Seagate a drive is merely a drive. You can mix and match them all you want, and so long as the RPMs match then they generally work. But with WD, if you do not match the speed, drive type, and sometimes even the generation, then you end up with annoying errors and issues to deal with. It does not matter so much with what you are doing, but it is something to keep in mind when thinking about expanding your storage (which is likely if you are dealing with 4K footage of any kind).
Hope that helps!
Caeden