Hi Brian,
I grew up on Lionel trains too, like many of us who never shook the train bug. I'm trying to work in HO now but have many friends that still do the "O" three rail. The post war stuff is wonderfully solid and therefore a great place for youngsters to start. It's also much more forgiving in terms of how well your layout gets built. Scale "O" like "HO" and "N" requires a bit more craftsmanship.
Regarding your question about three rail track, you may want to know that Lionel stopped making the old style tubular track last year. You can still get some of it, but turnouts are getting really hard to find. Note also that there are two types of the old tubular track. O-27 is the small, lighter weight, less costly track that can work with the old Marx track if you choose. O track is taller with bigger pins making it hard to mix the two. They are both "O" gauge meaning that your dad's trains will run on either of them. Also note that O track was made with more variety of curve sizes. Other than that, the old tubular track is a very workable system. Plus it's getting hard to find parts to restore the old trains, so if you like the searching part, you're going the right way.
My local hobby shop caries both Lionel Fastrack and MTH Realtrax. They also carry the Atlas three rail track which is very nice and noticeably more spendy. Fastrack and Realtrax are both good systems but they each have their pros and cons. They both make adaptor tracks to connect to the old O track. I'd recommend seeing what your local shop carries (hopefully you have a local shop) and talk to them and check out the options in person.
A couple final comments about getting into "O" or O-27. First, you can get more track in a given space than you might think. The "27" in O-27 refers to the diameter of the smallest circle. HO starter sets usually provide 18" radius track. That's a 36" diameter circle. That said, the trains don't look as good on such a tight curve and the buildings are still twice as big, taking four times the space in square inches. Second, three rail trains come in multiple sizes. The old O-27 (and new O-27) are built smaller than scale. This made it less expensive to get started and helps them negotiate such tight curves. Over the years, Lionel and more recently MTH and others have made trains that were a variety of sizes up to full scale. Not all of them look good when run together and most of the full scale pieces will not run on the tighter curves.
I hope that wasn't TMI. I'm sure you'll have fun no matter which way you go.
