Hi nydude,
You are right that things have changed a bit in the 10 years since you have been mattress shopping. One of those changes is that there are less actual box springs being sold (a mattress base with actual springs in it) and there are now more semi-flex mattresses bases being used (a mattress base which flexes just enough to absorb shock and increase the durability of the mattress but is not as big a part of the overall design of the sleeping system as actual box springs used to be).
A second change in this time has been the increasing popularity of specialty mattresses which use either memory foam or latex in their comfort layers (both of these are very different with memory foam more 'holding you in place" slow reaction foam and latex more springy and instant reacting foam which assists free movement). Polyfoam is the third type of foam which is usually (and most commonly) used in more traditional mattresses with innersprings and this is in between in terms of liveliness but closer to latex than memory foam because it’s also more instant reacting. Specialty mattresses are typically sold with a foam support core instead of an innerspring for support and most often use a rigid base which doesn’t flex at all). Of these types of mattress … latex is the most “springy” and closest to an innerspring feel although it’s still not the same. Polyfoam is the third type of foam which is usually (and most commonly) used in more traditional mattresses with innersprings and this is in between in terms of liveliness but closer to latex than memory foam because it’s also more instant reacting. In general, it’s also the lowest cost type of foam
Finally … the type of innerspring will make a difference. More mattresses today use pocket coils which are more motion isolating because the springs work independently while mattresses that use either Bonnell coils or Offset coils (generally higher quality and more expensive) will be more “bouncy” because the coils are atteched to each other with wires called helicals which means they act more “together” than "independently.
There are still mattresses being made in the old style (including two sided construction which is far less common in the major brands and chain stores) but they are usually available from local manufacturers rather than from major brands. The good news here is that local manufacturers as a rule make far higher quality mattresses at lower prices than the chain stores and major brands but they don’t advertise everywhere so they are a little harder to find.
So to get the “bouncy” feel you prefer inside the price range you are looking at … I would be looking for an innerspring mattress that used either bonnell or offset coils and that used higher quality polyfoam or latex in the comfort layers of the mattress (the top few inches) that was a little thinner and firmer than average and were made to work with a real “working” box spring (like the shifman).
Some of the better options in your area which would be worth calling to give them a description of what you are looking for to see if they made a mattress in your price range that had the feel you preferred are in post #2 here and post #7 here.
It may also help to read this page which is an article with some guidelines to help you avoid most of the traps and pitfalls of mattress shopping.
Hope this helps
Phoenix