If looking from the back the bearing assembly flops down when you turn the bars to the right, loosen one of the left barrels and tighten one of the right barrels. After you have fixed the 'flop' you can fix the barrels with the lock nuts and adjust the rear brake. That is pegs that slip on the axle and require the axle nut to be put on inside the peg using a socket and extension. Make sure you don't have any small washer between the peg and the dropout, it is best with the peg flat on the frame. Threaded pegs are not as good and will end up bending your axle quicker.
Pegs often come in either steel or aluminium.
Steel pegs are good for all round riding and should be able to take a few grinds. Aluminium pegs are mainly used by flatlanders because they are a little lighter, but are too gripy for grinding. Some mini ramp riders use aluminium pegs to slow their grinds down so they don't go off the edge. If you are buying new wheels or hubs there are a few more heavy duty options than a few years ago. Peregrine SuperPros with Suzie sealed hubs used to be the standard and where very nice for that day, but are not really designed for use with pegs.