Build your own computer from places online. If you’ve never built a computer or have no idea how to build one, try getting a barebones kit on websites like www.tigerdirect.com or www.newegg.com
If you want to build something that can handle UE4 decently well, then I suggest getting an intel i7 quad core processor. Probably something like a 4670 and up would do you nicely in the long run which is fairly well priced and can handle most anything you throw at it.
For a graphics card, I would get an nvidia geforce 750ti minimum to run it smoothly. If you can spot the extra cash for a 770 then I would because it’ll last longer and will allow you to do more within a level before seeing the chug of you computer. Especially when you’re dealing with high amounts of polygons and particle systems.
The motherboard can be your preference of size but it has to have the same socket type as what your CPU has. So choose what CPU you want based on price and then sort the motherboard by the same socket type and choose one with decent reviews.
Then take a look at what RAM speeds your motherboard supports and what the limit is per slot (ex: Max 4GB per slot x4 = total of 16GB of RAM). I would suggest having minimum of 8GB or RAM to be honest. 16GB of DDR3 will do you just fine. No need to get anything super fast, something around the 1600Mhz range should be perfectly ok for this.
After that, all that’s left is your power supply, hard drive, and case to get your bare minimum working. If you already have a decently new CD-ROM then I would just re-use that one. Or just pick up a cheap CD-ROM unless you use it regularly for stuff (I don’t which is why I have a $20 one in my computer lol).
Hope this helps!