... Just get a dedicated Blu-Ray player if your budget strapped ... or ... read on ...
My experience with playing standard DVD's through mythtv, erm, it's not really that good :)
Other people's milage may differ, but I've always found the interface lacking and buggy - often it just stalls, which is no fun when your watching a movie ... so ...
You can install Boxee on the same media centre PC, which is what I've done, and launch Boxee from your mythtv menu - nice and seamless. Boxee has a *much* better interface for DVD playing, in fact, it has a better interface for pretty much everything. We tend to watch any downloaded stuff through Boxee.
Also, get yourself a low profile VCR style case for your mythtv, although it sounds like you'll need a whole bunch of new hardware if your currently running myth on a standard desktop PC.
What you need is a mini-itx form factor - motherboard with processor on-board that doesn't require a fan for cooling.
This is what I setup a few years back, still going strong:
My missus loves it, sits neatly out of sight in the TV cabinet and is *very* quiet - hooked up via HDMI to the telly, ethernet cable to router (found wifi problematical and slow when copying files over)
Things are bound to have moved on a LOT since I got the budget rig above, so you can probably pick up everything relatively cheap on scan.co.uk or your favourite online hardware retailer.