If its old stuff, then your looking at standard definition formats of footage. There is going to be little point in capturing old poor-ish quality at the highest HD format. You may want to look into how to capture things in the first place ... for old footage, I would possibly be looking at the DV format and capture devices that can convert video into that format and transport it into the PC through firewire ports. This type of method is quite reliable and robust in doing this ... but you may be looking to get old equipment for that.
As to editing the files ... there is so much information on it, its not possible to put in a single post, or even thread. Basically, to get the high resolution formats down to manageable file sizes, the compression used is quite complex. In order to calculate that, the CPU has to do a lot of work. The same is true if you a compressing or uncompressing video data ... HD formats need a lot of effort.
Where hyper threading comes in useful is that because you have a large file of data, and the operation you're performing on it ( compress / decompress ) is going to happen across the whole file, then you can break the file up into chunks, and assign different chunks to different operational threads to be run by the CPU to be completed. Where an i5 might have 4 cores and 4 threads, an i7 with hyper threading might have 4 cores and 8 threads ... so the video work and be split 8 ways rather than 4 on the i7 ... in theory doubling the work rate ( but its not that much of a difference in practice ... but you get the idea)
Following from that, then you need to consider, how are you going to feed all the cores/threads of a CPU with enough data for efficient processing. IIRC Adobe suggest that for max efficiency on normal HD stuff, RAM should be in the region about 2.5Gb to 4 Gb per CPU core.
Then how do you feed the RAM? The video files come from the hard disks ... so the computer has to be able to get access to that quickly. As Milkie suggests, the common, effective method is to have 3 disks. One for the operating system and applications. One to store all your main video file data ( a repository ) and a scratch disk.
Video programs like to have data space to work with so that they can dump and access temporary data caches quickly as they need it. Having a separate disk for this means that this quick access is kept separate and doesn't conflict with the access to the main video files or applications. The scratch disk doesn't need to be massive either - but the faster the better.
Obviously your on a budget ... a scratch disk expense maybe something you can add later. I would suggest though that your video files are kept on a separate disk from the OS/App drive as a minimum ... that makes a big difference.
If its basic editing, then a decent video card will help in making the software display video smoothly for editing. Both AMD and nVidia cards offer acceleration for smooth playback in the likes of Premiere. nVidia has some more features for acceleration though the CUDA system, but they really only kick in for the more fancy editing effects.
All that being said, I used to have an 4core 2.66Ghz i7 windows 7 PC with 24Gb RAM, a 680GTX 2Gb GPU, 3x HDD system that i did photo and video stuff on.
For a number of reasons, I now have a 27" iMac. Its a 4 core 3.4 Ghz i7, 8Gb RAM an internal HDD and an external firewire HDD, and an AMD GPU.
To be honest, and because its a hobby from time to time, the difference in editing video is minimal between the machines. If anything, I prefer the Mac cause its all a neater package, even though the old PC may have performed a bit better.