Prepping garden question

Prepping garden question

Ok, so this is my second year gardening, and I've got a few questions about prepping the soil before we plant. I'm in zone 7 (I think? Seattle, WA). Our garden is pretty weedy right now - but most of it is grass, not anything flowering. We're planning to roto-till it next weekend, with a couple of inches of compost added. Do I have to rip up all the weeds/grass, or can I just roto-till it into the soil along with the mulch? Like I said, we pulled out everything that was flower or didn't look like grass. Secondly, we're planning on putting a couple of inches of grass clippings on top after we roto-till to help cut down on more weeds until we plant. Should we stick down a barrier first before the grass clippings? Thanks for any help! Last year we started from scratch so we didn't have these questions. Our garden is about 50' x 14'.
Compost

Compost

It’s cold, so cold. Well, for North Carolina anyway.

It’s cold, so cold. Well, for North Carolina anyway.

*new girl who used to be here and left and came back*

*new girl who used to be here and left and came back*

New gardener in Dallas, Texas.

New gardener in Dallas, Texas.

mystery plant ID

mystery plant ID

Hibiscus

Hibiscus