Looks like you have a well made bow. Just to be sure it's in good working order, inspect the back and sides of the bow for signs of any splinters starting to raise, and check the belly for compression fractures. They look like fine hairs running diagonally across the limbs. It's osage, so I doubt it will have either, but it's best to check to be sure. Osage can withstand abuse and father time better than any wood out there.
Next, use a string that is 3" shorter than the length of the bow, as measured across the back (outside of the bow), from string groove to string groove. Twist the string so you have a brace height between 5-1/2" to 6", as measured from the inside of the string to the belly side of the grip. If the brace height is below 5-1/2", you'll likely start to get some arm slap and arrow tuning will become difficult. If you go higher than 6", it puts undo stress on the bow and can result in the bow taking additional set. Also you'll probably find you get your best arrow flight with the nocking point somewhere between 7/16" to 5/8" above the arrow rest. Selfbows like moderately heavy to heavy arrows between 8 - 13 grains per pound of draw weight. If you load up with some 50-55# spine, 550 grain ash or birch arrows with 5.5" fletchings, you'll find the bow will be whisper quiet with minimal handshock, yet will cast the arrow very well and hit with authority.
Just a couple of general care notes on selfbows:
Store your bow in a comfortable "living space" climate. Wood can absorb and lose water, so hot attics, damp basements, directly over a heater, or anywhere at floor level is out. Always unstring when not in use. Be certain to evenly bend the limbs when stringing/unstringing. A bow stringer is the safest bet, though the push-pull method works fine, too. Stringing across the thigh is asking for trouble unless you are certain the GRIP is against your thigh and not the lower limb. Since the draw length is marked 27-1/2", make sure never to draw the bow beyond that. Also, be sure to draw the bow the same from the nocking point every time. Never goof around and pull the string from somewhere higher/lower. Overstressing the limbs from improper stringing, drawing, or overdrawing can damage or break the bow.
Selfbows...especially osage selfbows...can last a lifetime if properly cared for. You'll do just fine hunting with that bow. I've been hunting with selfbows exclusively for 5 years and am very comfortable with them. Having killed ten deer and dozens of groundhogs, and sitting on the knowledge that they've fed mankind for 10,000 years has assured me of that.
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