Your reel looks as if it has never been sharpened, so the biggest potential expense - replacing the reel when it is ground all the way down - is likely to be a long way in the future. If you want a good lawn finish you will need to have the reel and bedknife sharpened, and we don't know what condition the bedknife is in at this point. However I suggest you get it cleaned up, tune the engine, and get used to using it before you move on to blade adjustment and/or sharpening. Sometimes new owners spend money on sharpening before they have developed skill in adjusting and using the mower, and the result may be a wasted sharpening. You might try rotating the reel by hand and checking that it does not actually touch the bedknife at any time. Of course you need to ensure that your engine is filled with the correct grade of clean oil. Look at the foam element in the air cleaner to check its condition and cleanliness. Check that there are no squeals or clunks from it when you turn it over by hand, or when you start it. At that point you should be ready to tune it, inspect and lubricate the chains, and start mowing. One of your chains is very slack, and you will need to check whether it is worn, and if it is OK, adjust it with the sliding adjuster at the front of the chain case. Another chain's lower (front) sprocket looks rather marginal as well - it seems to have lost the tips of its teeth due to the chain being out of pitch, and the mating sprocket seems to have the same type of damage.
Your Briggs and Stratton engine has the Choke-O-Matic system. We can tell you more about the engine, including type and its date of manufacture, if you give us the long list of numbers stamped into the air cowl. We can also give you any tuning information you want.
