The best upgrade I could possibly recommend for an older computer (especially if you’re going to do heavy video work) is to put in a new SSD instead of the old platter-based HDD. You should see a dramatic improvement in performance just with that simple upgrade. RAM would be next on the list, because video/photo editing takes a lot of RAM. (Depending on your other specs, such as CPU cores and speed, it might be better/cheaper to upgrade your whole computer than to try to eke more life out of an outdated machine.)
I’ve used Lightworks quite a lot for video work, and it can do everything you want, plus a lot more! (It has a steep learning curve as well, which is fairly typical of any advanced video editor.) The free version is limited to 720p output though…