great potential.
I love the look of raised stone planter beds but know that they can be a budget breaker. You might consider wood as a less expensive alternative.

I think your site lends itself well to a quadrant layout - basically 4 beds , perhaps 3x5 each with a 3 foot wide path between each raised bed.

We're just about wrapping up on a small raised bed potager garden where budget was a concern. We built the raised beds out of redwood which naturally resists decay for a longer period of time over other soft woods.

We thought about using a composite type wood but decided on the redwood instead. You might want to check out the costs of composite wood. It will last a lot longer than regular wood and it is fairly easy to work with.

Attached is a photo showing a project that we're still working on, it shows the raised beds . We still have to attach the 2x6 cap, but you can get the idea.
Each bed is 3x5. There is a 3 foot wide path between the raised beds.

In regards to your existing brick , consider recycling it back into the landscape as paths or edging. {{gwi:52097}}From Figone

I think your first step should be a complete clean up of the area then a stump grinder guy to rid you of the huge stump. Perhaps install the bunny fencing and work on developing really good soil there - adding all the chopped leaves you can lay your hands on.

Some things to think about.

Bad soil does not grow weeds.

In my part of the world, plain kiln dried pine boards will have a lifespan of 5-10 years as part of a raised bed/planter.

If you live where rock grows wild, you can pick up a fair amount over time simply by keeping an ear to the ground. If you don't, it will be an expensive proposition.

The biggest problem with raised beds, is weed control of the area between the beds.

The second biggest problem with raised beds, is sourcing the soil to fill them. In most places, you do not want 'topsoil'

Deviant, your beds are beautiful, but I have to say I've never understood why people create raised beds with so much space between them. To save on filler soil? To allow easy access to the beds without bending? It seems to make it much more expensive and simultaneously wastes space that could be better used growing stuff! But I currently have no back trouble or other limitations on my ability to bend/squat/kneel, so maybe I'll feel differently when those problems arise. Is there another reason I'm missing? We mainly want to build up because of the stumps and roots in that area, in addition to the thousands of weed seeds we know are waiting to germinate (buckthorn, rose of sharon, privet, etc.). We were envisioning one big raised bed, instead of a bunch of smaller ones. I also personally find that weeds are less picky about soil quality than are cultivated plants and vegetables.

The town in which I live has fairly cheap compost available, so I was hoping we could just use that, mixed with some other stuff. Is that unrealistic? I'm sure it's not organic, but I'm hoping there wouldn't be too much nasty stuff on it.

Finally, I saw a comment elsewhere that suggested that an area with a ground stump couldn't be planted for "a few seasons." I have no idea why this would be. Anyone know?

Here is a link that might be useful: Amherst NY compost

Often times the function or needs of the space define the design.

In this case, mobility issues are a concern so the height of the beds relate to a comfortable sitting height.
The width of the beds accomodate a wheelbarrow.
And the more pedestrian pathways, the less room available for planting, which in this case was an emphasis. ... hard to beleive , but not everyone really enjoys to garden and only wants a few herbs and tomatoes for the kitchen.
I come across many people who only want a small gardening space and the rest of the area to be low to no maintenance , hardscape can fill that need.

Another reason that we decided to build raised boxes was the excessive adjoing tree roots. We did dig as much of them out as possible and then installed a perimeter root barrier - (very expensive) .
With the root barrier installed along with the various properly installed hardscaping, there is less potential for weed germination, making this a low maintenance landscape.
( This property is surrounded on all sides by very aggressively growing trees - many which are suppose to be removed by the HOA because they are causing excessive damage to the homeowners property ..... that's what you get when you plant a 'fast growing' tree - now they are paying the price )

In regards to your compost. - I'm obsessively picky about my soil mixtures. Luckily I have many landscape shops around that compete for the best compost so I don't have a problem finding OMRI compliant compost .
I would speak with the compost maker to verify their intake , mixing and heating process. It would be great if they were OMRI certified.

Whatever size you decide for your raised beds you'll want to be able to reach in from the sides. Ours are only 4' wide so I can reach from both & 11' long because that's the length of the 2"x8" wood we had gleaned. Any longer than that would be a bother walking around it. We used unfinished wood & realize it won't last forever.

We kept one path 3' and the others we did 24" because of the space available, but when the veg are in full production mid summer 3' isn't too wide at all and 24" is barely enough for me to walk sideways through.

If it's not all figured out by the time you want to plant you could always build one 4'x4' box & plant what you want right away. Sometimes the big plans are overwhelming & it's nice to have a small plan to start out. Check out Square Foot Gardening for a simple approach to growing your own vegetables & fruits along with protection from weather & rabbits. Your local library might have it, too.

Plus a 4' x 4' box could be moved easily once you decide to do something different.

My raised beds are built of cinderblocks. 4' and 3'4" interior width. I'm short and have short arms, so sometimes I wish the 4' beds were narrower.

Any longer than that would be a bother walking around it. I refuse to answer the question of length on the grounds that it may incriminate me. [Sometimes when there's an empty area I just walk across the bed; so far, that's feasible, as I only have one 32' section that's two blocks high.]

The aisles are 26", but because of the width of the cinderblocks and where I plant, I haven't had a significant problem with plants overhanging the walls (the pumpkins and cantaloupes are another matter, but that's my fault for planting them in the raised beds; next year they'll be in another part of the pasture). I'm a great believer in trellises, and grow vertically as long as what I'm harvesting isn't too heavy.

And yes, the aisles are weedy. Ideally I cover them in cardboard, which lasts about a year. [And ideally I am spending more time in the veggie garden as opposed to filling the front, back, and side yard with new beds for daylilies, ferns, and shade plants.]