| >>"My question is, what is the difference between different thickness's of strings?"
Different thicknesses are used for all sorts of reasons. Without me going into all the manufacturers, the thickness, or gauge is something you need to check out on your own to see what you like best. Maybe medium is a good place to start, say something standard like .45 .65 .85 .105. I don't use Fender strings, but they sell some pretty cheap sets that you can use for experimenting.
Also, bear in mind that a thinner string will probably have less tension than a thicker string when it is on your bass, this can make a difference in how you play them. This may or may not suit you depending on your playing style. If you attack the strings hard, then stick with mediums, the fatness and tension might suit you better.
Roundwounds have more character and gritty attack when playing rock if that's what you are after. Flatwounds are smoother, both in feel and sound. They feel slick compared to the roundwounds, and some have much lower string tension(Thomastik-Infeld). Lots of people like the lower tension, character, and playability of flatwounds. Once again, it depends on what music and style you play, and what kind of sound you like. For example, my favorite rounds are stainless Rotosounds. My favorite flats are TI's. Even the Elixirs are very comfortable, it's a unique type of coated roundwound nickel string.
Strings can come in different metals too, even coated ones. Stainless steel will be brighter and twangy, especially when they are new. I like stainless roundwounds myself for rock, I think they have a lot of character and bite. Stainless also need to be changed more often because they deaden in sound quicker. Nickel will be a little less lively out of the box, but the sound is more consistent longer. Stainless also makes more of that "wizzz" sound when moving up and down strings, so nickel roundwounds are a good middle of the road string. To really get a hold on the string "wizzzzz", go with flatwounds, they reduce it to minimum levels.
Also, you may need to make adjustments to your neck/bridge when trying out different strings. Look on the web for advice on adjustments, there's lots of good stuff out there. Sorry to make this one response so long, but the first question is a mouthful. Go to a local music store and see if you can spot some of the different kinds of strings I described on the basses on display. Try some out, see what feel and sound you like best.
>>"Do smaller strings give a more higher sound?"
Maybe a slightly different 'tone', but the same pitch. They should sound virtually the same when playing them. The biggest differences for me are the feel, the tension, and my attack. Also, different manufacturers concentrate on specific gauges and types of strings in their product line. They are trying to get their own share of the market, so there are differences in the final presentation of their products.
"Is there a recommended size you should use for each bass?"
Well, it's helpful to buy the right scale too, the length of the string. Most basses are 34". Measure(in inches) from the fretboard side of the nut(the grooved part where the strings enter the headstock) to the middle of the twelfth fret, then double that. I think that is the proper way to see what scale your bass is, but I may be wrong. Like I said, most like Fenders and other popular brands are 34". As far as recommended gauge or type, once again it depends on how *you* want them to feel.
I hope this helps. Can anyone else offer Cambass some info in string selection?
Good luck man! | 
My (Limited) Experience 
