Doing this on a college campus

You don't need anything fancy; nor do you need a lot of room.

See some of the comments on the ajoining thread about a potted herb garden for insights on how to get going.

There are very few herbs you can grow at all that can't be done indoors. As noted on the other thread, artificial light, either alone or as a supplement to natural light, is the best way to proceed.

As a space saver, you might consider a single-pot herb garden. One way is to use a strawberry pot, which gives you several openings to work with. That is, you can plant both in the actual mouth and in each of the side cups. But even that's not necessary. You can use a relatively wide pot (ten or 12 inches, for instance) and plant several complimentary herbs in it: basil, perhaps, along with oregano or marjorum, chives, tarragon, mint----whatever trips your trigger. I recently saw this approach done by grouping herbs by cuisines---an Italian mixture, for instance.

I would not include the herbaceious herbs like rosemary in a mixed pot, however.

Even if you go with a shop light and four-foot bulbs, getting started shouldn't cost more than about $20-25.

One additional thought. If you're going to do this using an existing window, in my experience the sills usually aren't wide enough. So you might want to build a shelf that extends out from the sill to give you enough surface area.

The jury is still out on aluminum, so I have no opinion either way. If you're concerned, line it with plastic first before filling with soil.

I assume you mean sealing the ends of the gutter and using it inside? Most of those herbs won't do well outdoors this time of year in most of the country. And, for reasons I'll get into below, you might really be better off with a row of plastic or terra-cotta pots anyway.

As to your list of herbs: All but the ginger should be doable. The ginger is problematical, for two reasons: first is soil depth. You need a lot of depth for the roots (which is the part you use) to mature. And, second, ginger is a tropical plant and requires more heat than the others on your list. So you wouldn't be able to grow them together. I'm working from memory here, but IIRC, ginger needs at least three years to mature even under good conditions.

I'm not familiar at all with lemon myrtle, so can offer no advice. The smallest container I've ever grown capsicums in was a 5-gallon pail. And that was outdoors. My mom used to grow an "ornamental" in a ten-inch pot, though.

The big problem with casicums is getting them to ripen. As with all fruits and veggies they require red light, and there's not enough of it in the winter sun. So you would have to use a grow light to provide it.

Mom's ornamental would be a case in point. Grown as a houseplant, with window light only, it would set fruit. But none of them ever turned color.

Capsicums are tropical perennials that we usually grow as annuals in North America. Many people do, however, bring them indoors during the winter. I don't know many of them who are successful having the plants continue to set blossoms and fruit until retransferring it outdoors in the spring. I know one case where the person has kept the same plant going for six years that way.

I would add, too, that if you're talking about only a single window your list might be a bit ambitious. You'd be talking about a "pot" that's only 30-36 inches long by what? three or four inches deep and the same across. And some of those really like to spread---the oregano and thyme, for instance. Others, such as the parsley, have large aerial parts. The crown of a single parsley plant, for instance, can easily fill an 8 x 8 inch space. The oregano I started last spring quickly spread to fill the 13 x 13 inch space allotted it. Depending on variety, thyme can move almost as quickly. However, if you use individual pots (I'd go with a minimum of 8" pots), each herb is confined to its own space, and can't crowd out the others.

Don't see why you'd need special equipment when you're at home---particularly if you can put the pots outdoors where they'll get plenty of natural light. Even if you have to leave them in a window, the summer sun's wavelengths such that they'll provide all the light the plants need.

The summer sun will be ideal for your capsicums, as well, and you'll likely get them to ripen.