First, a question regarding the 2007 Mini that you use NOW.
How much of the internal hard drive space have you used, during the years?
That's an important question because once we know it, we can advise you on what size SSD to get inside the new 2018 Mini.
DON'T buy a 2014 Mini. It's outdated and not worth the money any more, even though it "costs less".
That said...
You'll probably be very happy with the "base" (i3) 2018 Mini.
8gb of RAM will probably be "enough", although if you can afford it, I'd suggest getting 16gb pre-installed from Apple (we don't yet know what's Apple's RAM requirements for good operation are going to be 3, 5, 8 years down the road).
IF you haven't used up much space on your 2007's internal drive (less than, say, 75gb), you could probably do with the 128gb SSD. If you "need more space", you could buy an external USB3 drive (either SSD or HDD), and use that, and it will work VERY well.
IF you have used up more space to where 128gb would be "too tight" for your needs, I'd spend the extra $$$ and get the 256gb SSD.
If cost is a consideration, you might buy an Apple-refurbished 2018 Mini. It comes with the same 1-year warranty, same as new. Check this page:
https://www.apple.com/shop/refurbished/mac/mac-mini