The beauty of the Mini is it actually is pretty easy to work on.  It is one of the easiest iPods to take apart and the battery is very easy to replace. 

Also, you can replace the hard drive of an iPod mini with a Compact Flash Card.

 

The iPod Mini's for sale run about $75 to Buy It Now for a Mini in good shape.

There are some significant differences between the iPod Mini 1st Gen (aka 1G) and 2nd Gen (2G).  The 1st gen was a bit of a power hog and the battery could not power the iPod for very long.  Six hours may not be that far off for how long it could last.  For the release of the 2nd Generation Mini, the electronics were re-done which resulted in significantly better battery life.

How to tell if you are looking at a 1st Gen Mini or 2nd Gen Mini:
From the outside, there are 2 give-aways:  The 2nd gen has the size of the hard drive etched into the backside cover (such as 4Gig or 6 Gig, shows as 4GB or 6 GB).  The other thing is that the click wheel for the 2nd gen has symbols which are the same color as the case (pink, green, blue for example).  The silver Minis of both generations have gray symbols, so this can not be distinguished.

The two generations can interchange the same battery.  However, you can not interchange the clickwheels or the LCD display.

Internally, the differences can be seen in the size of the ribbon on the LCD display: the first generation LCD is wider than the second gen (which is why they are not interchangeable).  Also, on the first gen, there is a small seemingly pointless point right below the battery connector which is a black circle with a silver center.  A 2nd gen will have two small round components below the battery connector, the 1st gen only one.

The cases seem to be compatible or interchangeable but you have to have the click wheel which goes with the generation of your board.  If you mix them up, you will get an ipod frowny face.

A bit of advice on buying broken Minis: I have purchased on Ebay both Minis offered by a person who "just doesn't know how to replace the battery" or who "doesn't know what's wrong with my ipod" and this is OK.  The trickier sellers are ones who will put together a bad board with a bad drive and a bad clickwheel and a bad LCD.  These are people who have worked on Minis and are just trying to unload their garbage.  One lot of 3 Minis I purchased had absolutely nothing salvageable except the cases (and maybe headphone jack).  I should have known, the picture showed the iPods in pieces.  Don't go for those.

Part of the trick is, that sometimes the problem is the main board.  To buy a new main board for an iPod Mini is pretty expensive (like $35) so you can actually get a working Mini for less.  If it's a hard drive (which you may not know until you get it) it is not so bad because you can replace the hard drive with a Compact Flash easily (as mentioned above)