I currently have 205/55 R16 91V M+S Goodridge tires and an '06 Honda Civic Coupe. Should I stick with the same type of tires for go for something else? What's the difference between getting R16 or R17? Does it really matter? I realize I don't want anything above R19 on my car because it's going to be too low, but 15,16, or 17? Why would I want any of those sizes? Also, should I change the tires myself or take it somewhere so that they can be aligned etc?
As pointed out by DXM, the 15,16,17 isn't an interchangeable number.
None of the first 3 numbers can just be changed individually.
With your 205/55R16 example:
One wheel can hold a range of widths, so you might be able to go from 205 to 225 to run a wider tire (more rubber on the road, creates a larger contact patch and so theoretically more traction) but you would need to reduce the sidewall percentage to 50 to keep the height of the sidewall close to the same (112.75mm vs 112.5mm).
If you do not keep the overall diameter of your tire the same (wheel diameter + sidewall height) you will be altering your final gear ratio which will make your speedometer incorrect, alter your fuel mileage (better or worse depends on driving behavior and altered size), impacts your acceleration, what speed you can reach in which gears, your effective power band, etc.
Again using the 205/55R16 your current overall diameter is 519.15mm (wheel size * 25.4 + tire width * sidewall percentage)
To move to a 17" wheel assuming the same wheel and tire width, you'd need to use a 205/45R17 to get close but you'd actually be 4.9mm taller (off by about 1%). Fitting a 215/40R17 would get you 1.35mm shorter (off by about .25%).
Going with a wider tire and especially a wider wheel you have to take more into account as you may have clearance issues and either need wheels with a different offset or make use of wheel spacers.
There is rarely a perfect match when changing the wheel size but the more you can reduce the variance, the less you will impact items on the car that you shouldn't be changing unless you understand why you are changing them.
Also have a look at:
There is a performance / comfort tradeoff which can be decided depending on the usage. On a track lower profile is often better, but on the road not so much.
The choice depends on what you are trying to achieve with new tires and what's important to you. handling? ride comfort? looks?
These are the reasons people buy higher size rims:
You do realize that if you go to larger diameter, you'll need new rims as well. So staying at the same diameter could save you few hundred bucks.
As far as specific advice for your make/model, check out honda online forums and see what people are using in their cars. Just stay away from clowns who wouldn't recognize decent taste if it hit them in the face. 17" will probably be good on your car. I wouldn't go higher.
If you buy higher-size tires, you'll need new rims. If you buy tires/rims in one place like tirerack.com or discounttiredirect.com, they will mount the tires for free and ship you wheels which are ready to go onto your car. If you buy tires separately, you will need to have a professional shop mount them on your rims.