I think affordable may be hard as from what I've seen they all cost 2-3 times what you would see on a carribean cruise. But, most of the excursions are free and there is free beer and wine in many. My parents just went on a cruise from Budapest to Nuremburg and they had a good time. I'm not sure on the dress, but I don't think they were required to be "fancy". My mom actually needed hip replacement surgery and she was still able to enjoy herself on the cruise (found out after booking, delayed until she got back from the trip). They told me that it was mostly older people on the cruise and not many 45 and younger.
They are terrific! We went on Uniworld from Nuremburg to Trier on the Mosel and we've done the Rhone from north of Lyon to Arles in the south. They are casual; bring a sport coat for one night if you need to. Total relaxation.
River Cruising is a great Value. You can see the country, have your meals and touring including, and depending on the Cruise and Cruiseline you choose, your beverages and tips can be included as well.
It's unfair to compare a river cruise to a cruise in the Caribbean. A river cruise ship has maybe 190 people on board instead of thousands, the service and dining tends to be far superior, and it is a totally different experience.
"Affordable" is hard to define. Is it worth $100/night to have a room with a sliding glass door to a deck vs. a reasonable sized window that does not open? Is it worth saving $500 to take a trip in March/April with much cooler weather? What about airfares? Are you going other places or just to the cruise? Some cruise lines are offering inclusive airfare. Is it important to have free wireless/free beer/soft drinks at dinner? Those are the tradeoffs.
If lowest cost is the #1 item, try a Rhine cruise in the least expensive room during March or November/December. My experience has been with Viking. No dressing up--everything is included in the price (e.g. tours each day, travel to/from the airport with air booked through them, etc.), although they will ask about a voluntary "tip" to the crew at the end of the cruise (about 10euros/day/guest).
I can't speak to other cruise ships, except to say that they all "double park" on each other at popular places, so you get a chance at times to cross through another brand. I noticed for Avalon, for example, no outside balconies, rooms a bit "fru-fru" vs. Viking contemporary.