Which types of tomatoes are good for which dishes?
The general consensus is that for occidental-style, cooked tomato sauces - all of the sauces you mention are - you want to use the more plum-shaped, thicker-skinned types like Roma or San Marzano, NOT globe tomatoes, especially not the greenhouse grown, large, watery varieties. The more ripe, the better.

Also, good quality canned product (whole peeled, or peeled strips) is usually considered superior to fresh, due to them being canned at optimal ripeness which would make transporting them fresh impractical. I found that the cheapest brands often are sloppily peeled and/or not ripe enough and/or too sour, it is usually worth going for the 90 cent can vs the 30 cent can.

Also, do experiment with what part of the tomato you use. You could:

-Use it whole except the stem, and puree or strain the sauce later (does not apply to canned peeled obviously :) )

-Use everything except the peel (will need looooong stewing to deal with the seeds)

-Use the flesh, and also the juice strained from the seeds

-Use only the flesh (lot of tomato needed, and you might lose some of the umami from the juices)

Also, mashing vs pureeing vs straining can make a lot of textural difference.