There are plenty more than just the few listed but based on my own experience these would be the least likely to disappoint while you get a feel for gardening. While you can grow just about any herb in a container some are more difficult than others but basil is super easy and very versatile in the kitchen. If you plan to follow some canning recipes of mine you'll be sure to want to plant some basil as we will be using it frequently.
Beans, Eggplant, Squash and Cucumber can be trellised, "vertical gardened", even when planted in a container. You will train the vines to grow up your make shift trellis. A good item to use to make a trellis would be vinyl lattice if you have any or wouldn't mind buying some. Here is an example of trellised vegetables:
As you can see these people use trellis' that are supported by the outdoor wall of their home. I like this tote idea as it would work well for those who don't have any yard to work with to plant directly into the ground. If you have totes you can't find lids for that would be an added bonus here as you wouldn't need to buy any. I would recommend drilling holes in the bottom for drainage if they are not going to be covered as these are. You can also purchase planting bags off from amazon that work well. We ordered a pack of 6 last year and used a few of them for basil, establishing berry plants and even potatoes. We did not have much luck in the potato department though. Here are ones similar to what we ordered:
While I was looking up these bags I also found that there is a company called EZ-GRO Garden that are American made products with this same material. (The EZ Gro containers are less expensive than buying totes and allow airflow to the roots of your plants for healthier growth resulting in a larger harvest) It is difficult to find the raised bed on their website however they can easily be located on Amazon. https://www.amazon.com/Victory-Fabric-Raised-Garden-Feet/dp/B00CS8R11S/ref=sr_1_49?crid=1QAYCF85IFA5G&dchild=1&keywords=patio%2Bgarden%2Bplanter%2Bbox%2Bfor%2Bvegetables&qid=1589321366&sprefix=patio%2Bgarden%2Caps%2C181&sr=8-49&th=1
Another idea I came across that would work well for anyone who does not have a yard to plant in but may just want some fresh herbs or small amounts of lettuce was this spice rack with coco peat liners :
I would not recommend this for basil or dill as these herbs grow quite tall and become root bound easily but lettuce, parsley, cilantro, rosemary, thyme and even chives would do well here. You can also find window sill baskets that you can line with peat or in the past I have found planters that fit on the edge of a porch railing that you could also plant in.
There are so many options to vertical garden and if you have Pinterest it is worth looking at for an evening to see which idea works best for you. Try searching, "vertical gardening", "urban gardening", "container gardening" or "limited space gardening" and see what might work for you.