You cannot preserve just any salsa recipe (unless you're just freezing it).
Tomatoes are on the border between acidic and non-acidic foods. What this means is that they can be water-bath canned if they are sufficiently high in acid; but, if they are low in acid, they need to be pressure canned.
If you want to be sure to avoid trouble, follow a tested recipe. Salsa recipes will have a careful balance of low and high acid ingredients. Do not alter the proportion of acids (tomatoes and vinegar or lime/lemon juice) and low-acids (other vegetables, peppers, etc).
The recipe you choose should specify if it requires pressure canning or water-bath canning. One of those two methods must be used, though... you can't just put it in jars and save it.
For tested recipes, see the Ball Blue Book, the Ball website, or the National Center for Home Food Preservation.
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
In general, if jars are improperly processed or don't seal, you reprocess them exactly the same way you did the first time. This doesn't depend on the original recipe; you just have to do the exact same thing over again. In your case, since it sounds like your original process was hot pack, you would have to open the jars, dump out the salsa and reheat it, resterilize the jars, and reprocess.
But in your case, unfortunately, it's too late. If you didn't process it long enough the first time, you have to assume that it wasn't sterile, and treat it as equivalent to not canning it at all. Yes, probability-wise, your situation is safer than that, but you have to plan for the worst case, because you have no way to tell. Something may have grown in there. Canning just isn't a good place to mess around with safety.
And before someone chimes in and says it, yes, if you're the kind of person who eats things that have been left out way longer than is reliably safe, you could save it. It'll work out some fraction of the time, so there are plenty of people out there who can truthfully say "I've done this and never had a problem." But it could also get you sick, so I can't recommend it.