Potting soil is not needed, although organic matter may be. Start with a good reliable soil test so you will know what the soils pH and nutrient levels are. Your states Ag School Cooperative Extension Service may do that.

How much mulch is on that planting bed? An inch of mulch may not need to be removed while 2 or more may. Those "weeds" could be part of the organic matter the soi8l may need and could be tilled in or you could cover the area with newspaper or cardboard and more mulch and just let those "weeds" die and be used by the Soil Food Web to help improve the soil.

In addition to the soil test suggested above these simple soil tests may help as well,

1) Soil test for organic
matter. 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.
For example, 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 your soil will smell, to a point. Too much organic matter
can be bad as well.

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.

kimmq is kimmsr

Thanks! I added a picture in my post, if that helps. I will try testing the soil and drainage today. As you can tell I'm new at this, so it seems a bit daunting! I guess what I meant by potting soil was organic matter. We have a compost barrel that has been building for a year (leaves, etc). Should I spread that out before I till the soil and then add mulch on top?

Well, having seen the bed I'd not call it enormous nor weed infested. Plus the mulch is barely visible. You could dig it over in an hour or so and incorporate the mulch as you go. As Kimmsr says, you could dig the weeds in but if they are perennial or seeding that could cause more weeds. So I'd compost them and then return them to the bed later in compost form.

Since it's up against the house and next to a path you don't want the bed to be any higher. Adding soil is not only unnecessary for the plants, it could be detrimental to the wall and messy on the path.

Weeds are sure to sprout so I would lay down several sheets thickness of newspaper and mulch on top of that after putting in your plants. Or cardboard as floral said. It really works for me. We get lots of rain in the summer and so many weeds. Newspaper is the best! But it must be kept covered with some sort of mulch or it looks ugly and will blow around.

If your compost is done or fairly close to it, definitely dig that into your flower bed. Any undecomposed stuff can go back into the bin for the next batch.