There's a few types of salsa -- salsa fresca (aka pico de gallo, aka salsa cruda), which is "fresh salsa" and uncooked, and if made fresh, it shouldn't be too watery (unless you add to much liquid, eg, lime juice), but letting the vegetables sit after salting will start to draw out extra liquid and could become watery.
For truly thick salsa, you have to treat it like a jam, and cook it to release the pectin in the tomato. (or I guess you could use some other thickeners ... I've never tried. tomato paste, maybe?) You don't necessarily have to cook the other ingredients, too, but I personally like roasting the peppers and onions to sweeten then up and remove some of the extra liquid. (halve the peppers and seed them, lay them on a tray cut side up with the onion cut into wedges, roast 'til they're softened, then dump into a food processor and either pulse or liquify it, depending on how chunky you like it. And the skin falls off the peppers, so I leave 'em out).
You can do the same roasting with the tomatoes, and it'll be thicker from the food processor, but you won't get the same cling without letting them cook slowly in liquid to develop the pectin. If you roast the tomatoes, I like to use plum tomatoes, as they have more "meat" to the gel around the seeds, and take out the gel and seeds.
A standard tomato implies that there is a standard salsa, which there isn't - but let's stick with your specific case of pico de gallo AKA salsa cruda.
The distinguishing characteristic of salsa cruda is that it uses raw tomatoes - the cruda literally means raw. Since you aren't going to be cooking them, and since water is going to be your primary binding agent, you'll want to use plump, juicy tomatoes that have potent flavour when raw, and that just so happens to be those bog-standard globe tomatoes you see in the supermarket aisles. Of course, if you can get garden-fresh tomatoes, so much the better.
Cherry tomatoes are also a great choice - they're very juicy and a little sweeter than globes - the only downside is that for a chopped salsa (as in pico de gallo), they tend to make preparation much more difficult and messy. If you've got the time and patience, give it a try; cherry tomato salsas taste much "fresher" than those made from globes.
The other common types of tomatoes, most notably roma and pear tomatoes, are really meant more for cooking. That's not to say you can't eat them raw, but they don't have a lot of juice or raw flavour, so they don't make a good base for cruda. Roasted roma or heirloom tomatoes (especially fire-roasted) make a great addition to salsa, but of course, it's not really "cruda" anymore if you cook any of the ingredients.
Do yourself a favour and don't use the plum tomatoes in a can; they're plenty juicy but have almost no seeds and no flavour.
So, all in all, for pico de gallo I believe that regular globe tomatoes are the most appropriate, but any tomatoes with strong flavour and plenty of juice will do.
Best Answer
I wouldn't trust any store brand to omit seeds entirely; it's just not going to be a priority for them.
I'd suggest making your own instead. It's fairly easy and fast to seed tomatoes using a chinois, and to seed peppers using a knife. And it'll taste better, too!