When UE4 came out and back all through UDK I used:
12gb RAM
i7-930 CPU
HD 7970 GPU
Even though they’re old, especially the CPU and lacking RAM I had no problems with UE4 at all, the FPS were fine and the engine ran smooth so you could certainly build something cheap and get a great experience. I’ve since upgraded CPU and RAM as I found 12gb to be lacking when I want to use more than two heavy softwares at once, but it was definitely enough for UE4, I now run 32gb ram and a 4930k for better multitasking and RAM disk. The HD 7970 or similar is about 2 years old now and should be rather cheap I assume. It performs very well and I see no reason to upgrade it in quite a while.
While an SSD is great, I wouldn’t say it’s going to give you it’ll just speed things up, such as booting, loading and saving but if a 120gb is all you can afford you’re better off buying a larger HDD so you have enough for storage, possibly a smaller SSD to use only for OS and then a decent size HDD for storage purposes and softwares. If you can afford a 120gb and have some extra left I’d say the best option would be buying that(for OS and important softwares) and as big of a regular HDD as you can afford. When making games storage dwindles quickly.