Skip both the peat and the vermiculite. Vermiculite is unnecessary for any inground plantings and expensive. Peat can acidify the soil unnecessarily and provides no nutrient value and limited organic matter.

You are far better served with just adding compost, any combination you have, to no more than 25% of total soil volume. This provides a good nutrient base, sufficient water holding capacity, adequate organic matter and good textural content for drainage and aeration.

I would say things depend on your soil type. If it is fairly clayey, I have found that peatmoss can loosen up the soil very similar to compost....and it lasts a lot longer. Course you should add your compost also.

My local peatmoss isn't very acidic.

It's hard to tell you how much of anything you need to add without a soil test.

Isn't OK soil generally alkaline?

You also "should" plan for the long term, not just start-up. Lots of mulch can be handy and valuable in that plan.

Thank you for the answers. I should get my soil tested. I will see if I can find somewhere to do it nearby.
Ron

Where in the United States are you. This is a very large country with a very diverse set of soils and climates, although there are some things that are basic to anywhere. If your states universities Cooperative Extension Service does not do soil testing (most do) they will have a list of labs that will.
Most all soils I have looked at in the last 50 plus years lacked adequate amounts of organic matter, 6 to 8 percent. Some people think peat moss will lower a soils pH but that is not my experience. Tree leaves, pH ranges from 3.4 to 3.8, do not significantly affect soil pH so why would peat moss, pH in the 4.5 range, do so? Then the amount you have, 3 cubic feet for about 78.88 cubic feet of soil, is not enough to significantly change the pH anyway.
I would mix the peat moss and compost together and till that in, not concern myself with rehydrating the peat moss, and forget the vermiculite, and then water that planting bed well.
Conventionally grown cotton is among those plants that are heavily sprayed with pesticides and some are systemic types so much of the cotton burr compost could be laden with pesticide residue. One proponent states that spraying must stop so the pesticides can dissipate before harvest evidently confusing cotton with food. As best I can determine there has been no testing to find out if there is any pesticide residue in Cotton Burr Compost. So no testing to show there is or is not means claims can be made that there has been none found, you do not find what you do not look for.

I agree with the advice to use the peat moss (don't bother pre-hydrating, just water the patch after or wait for a rain), plus the compost.

I've used Cotton Burr Compost and it didn't seem to hurt my plants. Also the stuff we find around here tested very high in nutrients and organic matter compared to other commercial composts. I would not be afraid to use it especially if just mixing a few bags into an entire garden.

kimmsr, I am in NE Oklahoma (see my original post) near the boundary of zones 5 & 6. Mixing the peat moss & compost in sounds good. Cotton seed is used as food, and don't forget cotton candy :)

toxcrusadr, I'm not concerned with chemicals in cotton burr compost hurting my plants, I'm concerned with them hurting me and my family. If the spraying were stopped awhile before harvest, plus the time for it to compost, I would think that most products would be significantly degraded. I have other composts, so maybe it's not worth it. I can spread it on my yard instead of use in the garden.

Thanks
Ron