There are all sorts of ways to mount a ship model. Some modelers modify lamp finials, which you can buy at places like Lowe's or, if you have one in your neighborhood, a lamp repair shop. There are two problems with that approach. One - you usually have to modify the finial in some way, by chopping the top off and/or drilling the hole the rest of the way through. (It probably will come with a threaded hole in the bottom. Two - lamp finials look like lamp finials. My guess is that most of them are pretty tall for the job of mounting a Titanic model.
You might want to check out the mounting pedestals made especially for ship models. Two good sources are Bluejacket (www.bluejacketinc.com) and Model Expo (www.modelexpoonline.com). Most such pedestals are designed for sailing ship models; they have grooves in the tops to accommodate the models' keels. It wouldn't be hard, though, to hacksaw the top off the pedestal and file it smooth.
When it comes to baseboards, you have lots of options. If you know somebody who has a router, and have access to a source of nice hardwood (such as walnut, mahogany, or cherry), maybe you can talk that person into making you a baseboard with a nice, decorative edge. Here are a couple of sources for good-looking hardwood boards: www.woodcraft.com and www.rockler.com .
Model Expo and Bluejacket sell pre-routed baseboards, though they're a little on the expensive side. and the variety of sizes is limited.
Your biggest problem, if the model is almost finished, may be figuring out a way to fasten it onto the pedestals firmly. The best way to approach that problem is to worry about it while you still have access to the hull; you can either epoxy a piece of wood inside the bottom of the hull or mount a couple of sturdy nuts in it, to receive bolts coming up through the pedestals. I'm not familiary enough with the kit to suggest how best to mount the hull when it's already put together, but I'm sure there's a way to do it.
There's no rule that says the model has to be mounted on pedestals. Lots of very handsome liner models are mounted on keel blocks - a row of hardwood blocks, spaced fairly closely together, suggesting (though not literally representing) the keel blocks in a drydock. That method lets you epoxy the model firmly down to the blocks; for a model that's almost done and doesn't have any internal mounting mechanism, that might be worth thinking about.
Hope that helps a little. Good luck.