Total eradication of weeds will probably never happen but you can knock them back dramatically with repeatedly pulling up, digging up, cutting back or spraying. Some weeds are more effectively killed with Roundup at different times of the year. For instance, some plants take in Roundup more in the fall when they are starting to pull sap down instead of pushing it up. You will have to research your weeds.

Nature abhors a vacuum--if you remove the junipers, weeds will colonize the site. You'll have to plant something else if you want to keep the weeds at bay. You can solve this problem in a few ways, but here's what I'd do:

1) Spray the existing weeds with full-strength vinegar to kill the tops.
2) Mulch heavily with maybe another 3" of pine needles or bark. Laying black weed fabric underneath this mulch will help.
3) In spring, as soon as the frosts are over, plant a very hardy native groundcover.
4) Use vinegar to control weeds until the groundcover fills in.

Another alternative is what I've seen called a "lasagna mulch." You basically lay newspaper or cardboard over the area to smother the weeds, and then layer green and brown compost over it and just plant right into the mulch.

Here is a link that might be useful: Lasagna mulch