They're pretty good cars, but carbureted models (those without the -i at the end of the trim line) can be quite a pain to work on if you have to keep the factory carburetor. An easy fix is a Weber 32/36 DGEV or Weber DGES carb swap, which is available from Redline Weber.
Automatic transmissions can be an issue, but if you get a good one, adding a cooler and bucket flushing with Honda Z1 fluid (I've been told there's an "old" and "new", but I haven't had an automatic for quite a few years.
Manual transmissions tend to like either Honda fluid or Syncromesh. Mine has Wal-mart Super Tech 10W30 engine, since 10W30 is also a recommended fluid. You have to beat on one of these transmissions pretty hard to break them. One drag racer had few problems with his 10 second car with a stock transmission.
There are power upgrades available, as well as some suspension.
B16 intake manifolds fit the head if you block off a coolant passage and redrill 2 holes.
They have a lot of suspension travel. I mention this because at stock ride height, they're fairly capable offroad. One of mine will end up being a rallycross car.
They share the 4x100 bolt pattern that the Civics and Miatas do, so those wheels interchange, or will with boring out the centers.
Any one of the GRM guys can swap a B series engine for under a grand if they're thrifty. Mounts are less than $300, I believe.
If you plan on turbocharging the A series, I have a Mosselman cast stainless steel T3 manifold that I imported from The Netherlands. It's the only one in the US that's up for sale.
Let me put it this way, I want to replace my 2008 Saturn Astra with a good condition 3rd gen Accord sedan.