Do not only look for size: speed and load ratings are also important!
eg: 195/65 r 15 V 88 translates to:
width 195mm,
height 65% of width,
radial (as opposed to diagonal) construction, (diagonal tires are now nearly extinct - for a reason.)
speed: up to 240 km/h,
load: 560kg per tire.
The compete tire designation should be marked in your car's registration papers (although the new EU papers ae crap, they note only one random tire size, compared to the old german paper, which had every single rim/tire combination listed). If not, have alook at the manual!
I would not bother too much with "rotating": on a rear wheel drive car, front and rear tires should wear out rather evenly. On a front wheel drive, the front goes out first. You then have two possibilities: change the front to the rear when it is around halfway worn, and when all 4 are worn out, replace all 4 tires. Or you wear out the front tires, change the rear tires (which will have more than half of their profile left) to the front, and replace the rear tires.
This has one advantage: you will always have the better tires on the rear axle, where they belong. Total amount of money paid for tires will be exactly the same. You would NOT want your rear tires to be significantly worn more than your front: it's the rear that keeps your car stable... So IF you rotate tires, this should be done in rather short intervals. No problem with that: to inspect the brakes you have to take of the wheels, so rotating tires is best done during the usual inspections.*
also, not every tire can be rotated! Some tires have a prescribed rotation direction, others hace a designated outer side. When the rotation direction is marked, these tires may not be rotated diagonally, e.g. rear left to front right, only rear left to front left.
Should your tires wear out irregularly (outer or inner corners, in the middle...) and prematurely, something is wrong. Rotating tires might hide the symptoms a little bit, but else be useless. Get the suspension checked and aligned, worn bushings replaced, and inflate tires to proper pressure. (I alwalys go to the recommended pressure for a fully loaded car at high speeds, while most people will drive the 1-person-comfort-recommended pressure. Difference between these will often be 0.5 bar... Not only will your tires last longer with higher pressure, fuel consumption will also decrease.)
Concerning buying over the net vs brick-and-mortar-store: I always check prices online and then go around and ask at a shop if they can match the price. Often, they can, or at least come close. So they get the deal, and everybody is happy.
* This assumes inspection intervals of 10.000km, as common on older cars, and good, long-lasting tires like Michelin, which can last 50.000km. With long service intervals and crap tires, this tactic will not work.