The number of hours on the wooden prop aren 't too important, as wooden props don't have fatigue limits, and aren't susceptable to fatigue the same way metal props are. The condition in which it was stored, and of course it's present condition, are very important.
Check the bolt holes for corrosion from bolts, and look for any possible evidence of wood rot. Usually this isn't visible even if present, but always check. The same for brass tip or leading edge protectors. Look for loose rivets or any damage to the metal or wood.
Tap-check the length of the propeller using a small metalic object such as a quarter. Don't do it hard enough to mar the finish. You're looking for a distinct change in the sound as you tap. This doesn't work on wood nearly as well as composites, but sometimes it can detect a subsurface flaw. Be especially attentive doing this on wooden surfaces that have been painted.
Do NOT paint the propeller on your own, without guidance from the prop manufacturer. Get specific recommendations on any paint types, thicknesses, etc. Get assistance in painting the prop.
Previous posters mentioned the need for retorque; this is critical on a wooden prop. Whenever the prop isn't turning, Place the blades horizontally. Don't have them vertically, lest you get an accumulation of moisture in the lower blade and an imbalance.
Check the outer coating integrity; if it's checked or flaking away, it can allow too much transfer of moisture. It may need to be resurfaced. You cannot do this on your own if it's going on a certified installation.
Check the laminates closely for signs of separation or other weaknesses and damage. Check the boltholes for elongation, or wear. Check the tips for damage or cracking. Check the hub faces for flaws or imperfections. The opposite faces must be exactly flat, and parallel, and the bolt holes must be perpendicular. This is seldom a problem with established manufacturers, but there are a lot of propellers out there which are made by small shops or unknown makers. If you happen to have an STC's prop from such a maker, use caution.
Be absolutely sure the diameter and pitch, and serial number is appropriate and approved for your installation. Unlike a metal prop, you can't take this one back to be repitched. Propeller-engine combinations are very critical for purposes of balance and vibration.
On the subject of vibration, you'll likely notice a big improvement right away. Wooden propellers tend to dampen vibrations noticably, and aren't subject to much of the harmonic issues that limit metal props.
Consider getting some propeller cuffs or covers to protect your prop when not in use. Also consider some quality leading edge protection tape for your prop; it's more easily damaged than a metal prop. Many propellers already come with nylon or epoxy leading edges, and synthetic or brass tips. If your prop doesn't have these protections, consider having something done for the leading edge. It's worth it in the long run.
As always, don't reuse your propeller bolts. Install new bolts and hardware when putting on a new prop. Enjoy.