So you want to build an eBaike on a budget to commute on that: has a throttle, goes ~20 miles one way and you live in the mountains...

IMHO you need a mid-drive. The fact you want a no pedal throttle option pretty much excludes most prebuilt eBikes, so BaFang BBS## is your best bet. If you don't have a bike already, then it will be at least $800 plus the bike minimum. Really can't be done right for less than $1,200 IMHO.

You didn't mention your weight, but my experience says a 350W-750W BBS-02 will get you there if you are willing to pedal. Otherwise go ~$200 more for the BBS-HD (now you are at $1,400) and will probably need a larger battery too; more $$$.

How are those costs for your budget?

PS: I am currently in the process of completing my first custom bike build. The option of adding electric assist will be kept in mind when selecting the frame and components. It is clear already that the bike itself will be over $2,000. Adding an electric motor and battery will put my build at around $3,000, which is in the price range of a pre-built quality manufactured eBike. The only reason I'm going this route is because of optionality, throttle or boost button, and the ability to add/remove electric assist at will. The bike will be a killer pedal ride all by itself.