Most all of those grow in soil conditions that are not very conducive to the growth of grass so start with a good, reliable soil test. Contact your local office of the Vrigina Tech / Virginia State University USDA Cooperative Extension Office about having this done. Also dig in with these simple soil tests;

1. Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer you soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

which can help you determine what needs be done to your soil to grow a good, healthy stand of grass that is fairly weed free.

Here is a link that might be useful: Virginia CES offices

So what type of grass do you want?

What type of grass grows best in the climate that you have?

Is your lawn supposed to be bermuda, seems possible for your climate?

Clover is not necessarily a weed in a cool season lawn. It mixes nicely with fescue and makes a great turf.

If you are trying to grow turf grass, I would rarely recommend that you kill everything and start over. Typically through overseeding and lawn management - you can get a good lawn in a couple growing seasons. If you kill everything and start over, it will still take a couple growing seasons to have a good lawn, unless you install sod.

If you want to kill everything and start over, glyphosate (Roundup) is probably the best product. It is a broad-spectrum herbicide that has a low toxicity and short soil residual. It is unlikely that even with a well-timed treatment, you can kill everything with one application. There will be seeds that germinate later as well. However, you may be able to get rid of a lot of the existing plants and have less severe weed problems later if you do use glyphosate.

I would have to disagree with kimmsr's belief that weed problems are fundamentally soil problems. Many weeds do very well in the same soil that will support a healthy lawn or productive garden. Lets not forget that weeds are not biologically distinct from other plants, they are merely plants that we don't want.

Kat, how you list the individuals suggests they are not on your ground as individual areas and are mixed widely.
To try to remove one or more, would be an impossibility so the consensus would be you have to kill everything to ensure proper soil to plant.

RoundUp, the product mentioned, will kill everything it touches....but you would be able to plant within a week to 10 days afterwards.
Of course precautions about using it has to be followed.

After killing the groundcovers, you should give the ground there something to better accept what you wish to have there.
You might wish to roll your ground to level any depressions that are there and then put down a 2" layer of topsoil/compost/loam/peat moss to serve as a good foundation for the laying of sod or seed.

The rolling should be done when the ground is with winter moisture in it. So if you decide to roll, do it as soon as possible. Waiting for the ground to dry, then rolling, could possibly induce compaction of the soil.
Use a roller that is no more than 1/3 full and it should not be a burden to pull it over the ground. Otherwise, reduce the amount of water in it.