First, let me welcome you to the forum, and to the wonderful world of Krags.  Beware:  Krags are addictive, and tend to multiply in gun safes...

Inheriting a Krag is wonderful, especially when you know that your relative (grandfather in your case) actually carried it in military use!  Wanting to keep it and pass it on is equally wonderful.  If possible, please post some pictures of your Krag, including the rear sight, front sight, receiver showing the serial, stock cartouche, and overall shots.  That way, 1.) we can give you a relatively decent estimate of it's condition and value, and 2.) we can enjoy your Krag with you!

Some things to check:  First, take a close look at the bolt around the area of the locking lug.  You are looking for obvious cracks (usually caused by using ammo that is hotter than the normal Krag load).  Look down the bore using a bore light, or by removing the bolt and looking at a light through the bore.  You are looking for corrosion, dirt, plugged bore, or a ring in the bore.  Any competent gunsmith can check these things for you too. 

The ammo you should look for is Remington 30-40 Krag with 180 grain corelokt bullets.  This is the most common factory load and is completely safe.  Winchester ammo is also available, but less common to find these days.

As for the cleaning, clean the bore and metal with any decent cleaner like Hoppes #9.  Oil with a good oil like Hoppes or Remington oil.  Clean the wood with any decent furniture or wood cleaner.  Stay away from anything that would strip a finish.  IF you disassemble to clean it, DO NOT try to snap the handguard off.  You must remove the rear sight first, then remove the barreled action from the stock, and finally slide the handguard off the barrel.  Reassemble in reverse order.

Welcome aboard

Thanks for the info.
Here are the pics you suggested.
I'll post pics of the bolt and magazine after this one.

Well, it appears that you have a very nice 1898 rifle that has not been fiddled with, as so many have over the years.  It has the 1901 rear sight, which some find to be best when shooting competitively (I prefer the 1902 myself).  Have you looked in the butt plate trap?  you may already have the cleaning rods and oiler.  The circled P behind the trigger guard is the proof mark, which indicates that the rifle passed the proof firing.  The cartouche on the left side of the stock is the acceptance cartouche indicating that the rifle passed inspection.

There should be three rod pieces.  The oiler goes in first into a small well, and then the rods are inserted into the three stock holes.  Most people put a couple patches or maybe a piece of paper towel in there before closing the trap.   This keeps the rods from rattling.