I like to reference the Park Tool website for bike repairs. They can be found at www.parktool.com and have information for just about all bike service and repairs. All of the bike shops mentioned in the links section will be able to make these adjustments/repairs.
Having a bike that won’t shift well can be frustrating, here is some information on minor adjustments to make your
bike work well.
Rear Shifting
Place bike on an indoor trainer with no load on the rear wheel. While turning the cranks, shift bike 1 gear at a time up and down to determine if the problem is with shifting to larger gears (physically larger) or smaller gears.
If you are having problems shifting up to larger gears then your shifter cable is probably a little bit loose and should be tightened ¼ turn at a time until smooth shifting is achieved. This will be the issue most of the time.
If you are having problems shifting down to smaller gears then your shifter cable is probably a little tight and should be loosened ¼ turn at at time until smooth shifting is achieved.
You may find that after you adjust for one shifting direction the other won’t work correctly. You may have gone too far with the adjustment or the cable may be sticking in the housing. If the cable is sticking then you will need to replace the cable and/or housing. That should be left to a qualified person if you are unsure of your mechanical abilities.
The Park Tool website explains rear shifting in detail.
Gear Sizing
It is in my opinion that most peoples’ bikes have too much gear for their riding ability. Most riders are not strong enough to use a 53 tooth big chainring on a 700C bike or a 56 on a 650C bike. With whatever front chainrings you are using, this is how I would determine what gears (cassette) you would use in the back.
Determine what kind of terrain you will be riding on. Will you be riding on flat roads or hilly roads? Now think about how fast you will be riding and what gear you are currently using for 90% of your riding. Are you near the center of the gears in the back? Mostly on the big ones or small ones?
If you are near the center for most of your riding you are probably already on the right gear combination. If you are on the smaller ones and there isn’t much climbing then consider going to a smaller cassette, you may be strong enough to pull it. If you are consistently on the larger ones then considering going to a larger cassette or smaller front chainrings. Having the ability to shift to an easier gear without dropping down to the small chainring is a nice luxury. A 12-23 is a standard combination, I don’t like the 12-25 because you only get 2 more teeth than a 23 and lose the 17 tooth cog that is important to faster riding, I feel it is a poor compromise. If you need more gear go for the 12-27. You will use it for hilly races as well as training and not waste money on an extra cassette.
Brake Tuning
Having brakes that rub or don’t stop is annoying and dangerous. Here is some minor information that can help tune braking better.
Inspect your bike’s brake pads, they should have not have significant wear on them. If you feel they are worn down and need to be replaced, have a bike shop or experienced mechanic replace them for you. Toeing and aligning brake pads is tedious at best but without an experienced person installing them braking situations can be dangerous.
Inspect the alignment of your wheels in the fork and frame. Make sure the wheels are centered in the fork dropouts and/or rear dropouts.
Inspect the wheels for side-to-side motion. A wheel that is untrue can rub the brake pad(s) in one or more places and make hard braking unpredictable. Truing the wheels may be necessary before making brake adjustments.
Brake pads will wear slowly and can be tightened with the barrel adjuster (located on the brake caliper) on an as-needed interval. If you find that you have to pull the brake lever further than normal, then you can turn the barrel adjuster out a little bit to tighten up the brake as needed.
If you find that after releasing the brakes that they still rub on the wheel then you may have a cable sticking in the cable housing. Replacing the cable and/or housing will probably solve that problem. Other solutions may include rebuilding brake caliper and/or brake lever. An experienced mechanic should perform those repairs.
The Park Tool website explains brake maintenance in detail.