The important thing is that you use good ripe tomatoes - if they're still hard, the soup will just be thin and flavorless. I always buy them when they're really red and give a little when you press them. The skin is honestly no problem, like the others already said - after 20-30 minutes of cooking it dissolves and you can just push everything through a sieve. That's way less work than blanching them first.
The trick I'd really recommend: add a good pinch of sugar right at the beginning, but not much - just a tiny knife tip amount. I know that sounds weird given your problem, but it's got nothing to do with sweetness, it actually helps the natural tomato acids come through better. Then the flavor balances out much better. And yeah, a splash of white wine or balsamic helps too, but only taste it at the end before you commit to anything.
One more thing: sauté the onions and garlic before the tomatoes go in, that makes the difference. Just briefly in butter or oil until it smells good - then add the tomatoes. Go easy on the salt at the beginning because everything concentrates as it simmers. At the end you can add fresh basil or cream if you want, but honestly you don't really need it.