Hello Wyatt's Dad,
It sounds like you're just getting started, so there are many, many options open to you depending on how much you want to spend, how much time you want to put into it, and what you want for an end result.
First, if you want to only use the DC wall transformer that came with the polar express set, you will be very limited. this small power supply is not designed for much more than the starter set it comes with. It will work for other LionChief locomotives, and LionChief Plus locomotives, however I found it did not have enough power to fire the remote couplers on LionChief Plus. the wall-pack is also DC, where most O-gauge engines, that are not LionChief, run on AC. LionChief run on AC or DC. Long story short, if you are looking for a new engine that is any better than the one you have right now, you will need a better power source. You can find suggestions galore by using the search function here and looking up transformers. If you are looking for something brand new, I'm partial to the CW-80($149 MSRP, $75 Auction site) or GW-180 ($279 MSRP, $250 Auction site). From MTH you have the Z-1000($129 MSRP, $99 Auction site) which is comparable to the CW-80 in power supplied. If you are on a budget you may be better off going with a used post-war style transformer. These are perfectly safe to use as long as they are in proper working order. I Like the ZW which sells for about $160 in a fully refurbished working order or the KW which goes around $100. Forum sponsor TinMan3Rail.com has had very competitive prices on nicely refurbished transformers, but I'm sure there are others here as well.
(EDIT: Forgot to mention that you should use TVS diodes with older transformers to protect the modern electronics from voltage spikes. these cost less than 50 cents and you can learn about them by searching TVS here on the forum. )
When it comes to choices for a new locomotive, the options are even wider than those for transformers. Are you looking for an exact replacement for the 2-8-4 Berkshire locomotive that comes with the polar express? Are you just looking for another steam engine, but not particular on what type it is? Are you looking for new products only, or are you willing to buy something a bit older?
If you want an honest to goodness, polar express locomotive, you are pretty well stuck with the one you already have, it's conventionally operated predecessor, or the full scale version that is rather costly. Another option is to look for simply the same type of locomotive, the 2-8-4 Berkshire. You tend to be in luck with this option as many of the models of this type are based on the real locomotive Pere Marquette 1225, incidentally the same locomotive the writer of the Polar Express used as the model for his artwork in the original story. Both Pere Marquette 1225, and Nickel Plate Road 765 are operating 2-8-4 Berks that you can still see today. In addition to these road names, there are many other modeled over the years.
The MTH option may be a good fit for you in the desired price range. I'm not very well familiar with their products right now, but generally speaking if you like it better than you like someone else's product, buy it. To gain control of all of the features offered in an MTH Proto-sound 2 or 3 engine, you will need to invest in a DCS system as well. Access to the basic features such as whistle, bell, and speed control can be gained with the 'Remote Commander' which costs about $60, but is limited to controlling ONLY one locomotive on the track at any one time.
Another option is to purchase a used Lionel TMCC Berkshire locomotive. The sounds are not as good as the newer stuff, but these are still very nice engines. I paid less than $200, shipped, for my TMCC berkshire which you can see and listen to HERE. The original TMCC command base and remote set can be had for under $100 now as well, or you can run the engine in conventional and still get the nice chuffing, whistle, and bell.
If you are NOT dead set on a 2-8-4 Berkshire locomotive, but are instead open to the idea of other nice styles of steam locomotives, you really open the door to low cost options. First, you have all the MTH RailKing and Lionel TMCC engines that are out there in your price range. In addition you could use a LionChief Plus Locomotive. The sounds are quite a bit better on these than on the standard LionChief, and the constant speed control and low speed operation are fantastic.
A LionChief Plus Hudson(4-6-4) or Pacific(4-6-2) list for a bit over $400, but are readily available for $300-350 form forum sponsors and elsewhere. Going with the LC+ option has a few benefits over other choices right now, in that you don't need to invest in another control system, and a new transformer is not quite required yet... though you may not be able to use the electro-coupler. On the other hand, if you think you will be investing in a full on command system such as Legacy or DCS, you'll have to keep in mind that those systems can not control the LionChief/plus engines. only the remote that comes with it will run the engine at this time... or in the case of LionChief Plus, it can also be run in conventional transformer control mode.
JGL