The good news is both of them are easy to grow indoors or outdoors, and they're perennial. Perennial herbs include rosemary, lavender, marjoram, tarragon, sage, mint, parsely, lemon balm, chives, sorrel, yarrow, chicory, savory, bay laurel, lovage, hyssop, anise, chamomile, bergamot, alfalfa, clover... the list goes on. You can use them fresh, or make your own dried herbs.
On top of that, variants of thyme work as a hearty no-hassle replacement for grass, and it even flowers.
A tangential word of warning for anybody feeling inspired to DIY some fresh herbs: mint spreads very aggressively. If you want to plant some, put it in a pot on a patio or pavement to stop it from getting into the ground.
If you do not, in a few years you'll have mint growing absolutely everywhere.
Mostly kidding, I grew up living at a rural property that had mint all over the place. I loved it, but I do understand how much trouble invasive plants can cause.
Do you have a recommended place to get those? Also, I’ve got clay soil here, and thyme has never done well for me. I’d love to replace swaths of my lawn with it, as I really like it’s appearance and fragrance, so any link to those varieties would be much appreciated.
Clay soil's definitely not gonna work for thyme, it's way too wet and nutrient-dense. You could try double-digging to remediate it, but that could possibly lead to other issues.
As for where to get stuff, search for plant nurseries near you. They may not be tech-savvy so you might have to use the old-fashioned technique of wandering around and asking people (anyone who works in dirt: farmers, gardeners/landscapers, contractors). They will know your local environment and what works best for it and can order plants and seeds for you.
It may not be practical for you, but you could try a hydroponic system like AeroGarden. I was given one last Christmas and grew lots of herbs (I've just moved and haven't unpacked it, but when I do the herbs will be coming out again).
AeroGarden is a pricy brand, but there are probably cheaper ones that do just as well.
I’ve been looking at doing something similar and the best advice I’ve found is from a local agricultural school and some local businesses that supply native plants in your area.
On top of that, variants of thyme work as a hearty no-hassle replacement for grass, and it even flowers.