Thickening comes from reduction. No need to drain the tomatoes and waste the delicious juices. Simply purée the tomatoes first, either somewhat or fully, or break them up with your hands, before starting the sauce. Not necessary, but to keep roughly the same volume you can use a bit extra diced or whole tomatoes, say one 14oz can per two 28oz cans.
If you choose to use paste get the best you can. Inferior pastes taste inferior because processors cheat in underripe tomatoes. These underripe flavors concentrate during processing. Another two things, if you choose to use paste: I'd suggest not more than 1/3-1/2 of a small can per 28oz can of whole or diced. And, after sautéing the aromatics (onion, garlic, etc.) add the paste and cook it. It should deepen in color, nearly brown. If using wine add it next, mix well, then reduce till the wine is nearly gone. If not adding wine add your tomatoes after the paste browns. (Scrape the aromatics and any vegs you have in there to the sides of the pot when browning the paste. Incorporate after adding the wine or the tomatoes.)
Contrary to the myth of Italian nonnas cooking all their tomato sauces for hours and hours, most are not cooked that long--unless tougher meat cuts are to be cooked in the sauce. (Tender meats that are being cooked in the sauce require a shorter cook time, obviously.)
Generally, tender meats, sausage, meatballs, etc., are browned first in the pot then removed. In their rendered fat the aromatics are cooked, the tomato sauce made, then the meats returned to the sauce to cook while the sauce reduces. When the meats are done the sauce is done though, if you prefer and if further cooking will not deleteriously affect the meats, you can cook very low for longer. When adequate reduction is achieved cover the pot, or partially cover, so as not to over-reduce. Should this occur simply add a little water. Skim the excess fat that rises to the surface.
Quite a few cooks do not actually brown meats like ground beef or pork, or meatballs, the just cook till the exterior raw look is gone and some fat is rendered. Like for chili, this is to prevent the development of firm, brown surfaces that then affect the texture of the finished sauce.
For tough meats--say, short ribs (which are terrific slow-cooked in sauce), lamb shoulder or shanks, oxtails, et al., longer cooking is required, as you'd expect. Often something like sausage is first browned, whole or sliced, then removed, then the short ribs or shoulder or shanks or tails are browned or simply colored, then removed, the aromatics are cooked and the sauce made, then the meats go back into the sauce for long, slow cooking till they are tender. Meat on the bone is often removed from the pot and allowed to cool, the sauce skimmed of excess fat, the meat removed from the bone and shredded, then returned to the pot.
Note that for long cooking sauces it is best not to add basil early on (it tends toward bitterness if cooked for long). Save it and fresh parsley for the last 5-15 min of cooking.