Make sure the downspouts will flow. Perhaps some pipe (like the way you have handled the DS in the second pic) that flows out through the wall.
Find out how high a wall you want. Use a level, start 6" under the siding (or more) and see how high that is out where you want the wall.
Vegetable beds (and any other growing bed) will be MUCH better if you do not walk on them, so test-reach, pretend there is a wall there, how far can you reach without leaning on or stepping on the soil? Most people can reach 2' pretty well, and might stretch a bit, but that stretch is hard on your back when you want to do a lot of work that way.
You can remove the rock (Use it for drainage behind the wall, or for a walkway in front of the wall) and add soil & compost blend to make the area level. Make sure that is OK with the gas company. Don't bury any critical part of their meter.
Wall materials:
Wood (any sort) rots over time. Some kinds can last for many years. If you only want to go a foot high you could use a 2 x 12 board and 3/4" pipe or other cheap way (looks cheap) to support it. Better (if you want wood) is to use 4 x 4 posts 4' on center, with or without concrete in the holes. Check local building practices. I work in an area with no frost heave, no snow, and posts are typically sunken about 2/3 of the height of the wall for small walls. Might be different in your area.
Concrete (many variations)
If you just want a foot to 18" then look into the home-owner quality (non structural) gravity block walls available in the local hardware or masonry yards. Names like Versa-Lok, Allan Block and many others. Ask about what sort of footing they need (another way to use up the rock!) and how to build it as high as you need. More than about 3 blocks high I would not trust the small blocks sold for small, decorative walls. Larger (structural) blocks made by these companies will work for much taller walls. They are usually pre-engineered for walls up to 3' high, and can be engineered MUCH higher. You will need to make a rock base and bury at least one block, but ask about local practices. The lightweight blocks tend to shift over time, but are easy enough to rebuild. And quite easy to get into if you need to dig out the planter (maybe a plumbing leak or something). The larger blocks are less likely to shift, and a bit more work to re-do in case of emergency, but can be done.
CMU block is a much more permanent wall. It involves pouring a footing, building the block wall, filling it with concrete. It includes reinforcing bar. There are decorative blocks (ask about Split Face blocks, and different colors) or you can add a stone or brick veneer and cap. Much more expensive, but it never has to be redone. A poured in place concrete wall is similar. Neither of these will look good if you have to break into it and dig out some broken plumbing or something.
Natural rock about a foot in diameter or less can be stacked up to make a dry stack (no mortar) wall. Going a foot to 18" high is very easy. Just sink the first course a few inches (again- check local practices!) and set the next course in place by laying each rock over 2 of the ones below, like bricks, so they lock each other in place.
Very easy to rebuild if needed. Not so stable to lean on when you want to reach inside the planter ares. Can be very nice looking in a rustic sort of way.
Railroad ties, landscape timbers or other rustic wood: Can certainly make a wall like this, but some (rail road ties) are often treated with creosote to prevent rot. Some people do not want to grow vegetables in soil next to creosote. If this is not an issue, then dig the first one in a bit, drill holes through it and use pipe or reinforcing bar driven a couple of feet into the soil to stabilize it. Drill the next course into the lower course. Might not need more than 2 courses.
In anything where you have to dig into the soil make sure you call Underground Alert Service to mark pipelines. I can see the gas meter, but which way does the pipe run? Any other services? You might not know about them all.
