What is the best pot and way for this to avoid chemicals leaching from the pot/container into the plant?

I have been growing tomatoes, peppers & other veggies in pots for a few years now. Some are plastic & some terra cotta.
Can't say I've noticed any difference in the veggies.
If it's really a concern for you, go with terra cotta.

Herbs tend to actually like pretty lame soil, heat, and dry conditions. They're often not fussy (an exception--mints, which LOVE lots and lots of water!)

Stuff like rosemary, thyme, and oregano go well in terra-cotta (or fake-a cotta...terra cotta is HEAVY!) pots without much fertilizer, though they do like plenty of light and warmth.

Now, stuff like tomatoes needs more water and a little more fussing over in terms of removing pests (like, say, slugs eating your fruit.) Food tends to need more fertilizer, but if you use chemical fertilizers SPARINGLY or well-rotted manure or compost, you can get your plants the nutrients they need without burning them up or causing nasty run-off issues.

It's generally not so much of a problem when you put fertilizer ON plants...it's the run-off that's really a problem. On a large scale, it can cause rampant algal blooms, red tide, excess water plant growth...it's bad stuff.

Get good soil (I prefer the soil marked "topsoil" over "potting soil", because potting soil tends to be either way too light and fluffy or too sandy.) Put it in non-reactive pots/tubs (beware galvanized tubs rusting out at the bottom), and prune/remove dead leaves and bugs on sight.

And if the container says, "not for food use"...don't use it to put any food plants in. That generally means it has lead in its glaze/paint or some kind of unstable coating that won't stand up to dirt and moisture. Same goes for "decorative use only."

Go to the garden section and pick up genuine gardening pots...it doesn't have to be expensive or fancy or even all that pretty. It just has to be durable and suitable for food plants.

And go easy on the chemical fertilizers and pesticides, 'kay? Some pesticides CANNOT be used on food plants, period (only ornamentals.) Some pesticides can be used on food plants (like Sevin dust) but only at a certain time (that is, you have to stop using it a certain amount of time before harvest so you won't eat the residue.) And no herbicides, period. You see a weed in a pot, you pull it out. No Roundup for you!

Just experiment and keep all chemicals to a minimum and see how it goes...gardening is fun even when it's a big failure!