The slices are as thin as I can easily make them, a bit thinner than for dinner, so are about 3/8-inch thick or thereabouts. Sometimes I get only partial slices but don't worry about it as they all taste as good whether it's full slices or part slices. Cherry-type tomatoes are sliced in half or quarters. The most important thing would be to be consistent for size on a particular batch so they are ready at the same time. You definitely would not want thick and thin or quarters in the same batch or some would be over-dried and would lose some of their quality. They are ready as soon as they readily break or crumble.
For drying, I usually slice them first thing in the morning, leave them out in the sun all day and then in the dehydrator overnight. It will vary depending on your humidity as well as the type of tomato (and thickness of the slices). Just keep them going until they are completely dry. I seal them in vacu-seal bags which is probably a mistake because I usually put quite a few in each bag . . . a mistake because once I open a bag, I eat them all in less than a day or two! Better than candy. So far, none have made it to salad, noodles or sauces. They can be stored in glass jars with the lids fastened tightly; I will use canning jars with a used (but not bent) sealing lid with the ring when I use jars. My book recommends putting any fresh fruit dried with peels left on in the freezer for at least 48 hours to be certain any possible critter eggs are killed. Though I don't worry about that, I still do it after they are in their storage container. All of my fruits/veggies are dried with the skins on. Plums, grapes, etc., are cut in half.
Type? Romas are by far the best; they slice so very nicely and "behave themselves" on the racks. I don't like them fresh at all; they are definitely a cooking tomato. However, all tomatoes are good dried, but the juicier ones are much messier to prepare when fully ripe. They sweeten when dried; the flavors are more intense. Until I dried my first ones in 2000, I had not eaten dried tomatoes and didn't understand why people liked them so much. Well, now I know. I still haven't eaten commercial ones, however.
All tomatoes can be dried; however, I usually can the others because they are so much bigger. The diameter of the Romas lend very well to slicing and can be sliced thinner as they are a meaty tomato as well as giving consistent sizes. I've dried nearly every variety as most of mine are heirlooms and there are never less than two dozen varieties in my garden any year. This year, for instance, I have nearly a dozen of cherry-type heirlooms as well as many full size tomato varieties.
All the preserving directions say to use firm fruits. That is good; however, I don't worry about it if they are a tiny bit overripe as long as they dry properly. My thoughts are that any that would be preserved by canning or sauces are good for drying. Others might or might not agree.
Beware of dried tomatoes . . . they are addictive. I plant Romas just for drying though I also can sauces made with them. I'm so very anxiously awaiting ripe Romas, lots of ripe Romas, so I can feed my addition.
I hope all your questions are answered, and maybe some you didn't think to ask. Happy drying.
Glenna