My 2 cents: consider a saucier shape vs a saucepan - maybe you like it, maybe not. For a saucepan, consider Tramontina. the Wirecutter recommends them with an All-Clad saucier as an upgrade pick.
I'm also a longtime Revere Ware user with a workhorse 3-qt saucepan. Mine came with steamer and double boiler inserts and I think I forked out a major investment of $20-25 at a Revere outlet store for my first college apartment. I still use it with those inserts on my gas cooktop but the bottom had become so warped that it was kind of useless on my portable induction burner. I decided to replace it with an All-Clad stainless 3-qt saucier (their lowest level stuff) that I ordered from homeandcooksales.com for $85. They sell factory seconds in now-and-again sales events so it may not suit your immediate need as they just closed their last November sale. No lip, spout or helper handle so it fits in the dishwasher as well as the Revere Ware. It was a very nice upgrade and I subsequently replaced my 1 qt and 2 qt Revere Ware saucepans with All-Clad sauciers and have been very happy with them. I very much like the more rounded corners for the things I tend to cook in them. I've had good experiences with several purchases from those people but $85 is still over your budget, hence my recommendation to check out the Tramontina. I don't have it but do have a nice skillet from them. Unfortunately it's not induction compatible, so check that out if it's important to you.
