It doesn't really effect the saxophone or the noise. The difference is the thickness or thinness. The smaller the number… The thinner they are. The higher the number the thicker they are. If they're thicker they're harder to blow into. If they're thinner they're easier to blow into. You know what number you need by you're experience or how long you've played. I hope this helped you!

P.S. I'm a 2 and I've been playing since September
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The higher the number, the harder the reed.

If you have been playing less than a year, I would suggest using a 2 1/2 and then move up to a 3 after a year. Once you gain stamina and playing experience, you want to find a reed that is harder and on the edge of being a little hard to play. You should feel back pressure. (Moving up in reed strength is not related in any way to your skill on the instrument (at least it's not past the first year). Beyond that, you want to find a reed eventually that gives you a good sound with a lot of core (full, "strong" .. not airy, whiny and weak) …. As you develop over the years if you continue playing, you can look at your own aesthetics of the sound that you want to go for.

Harder reeds (in general) help you to create a fuller, thicker sound, however if you are new to the saxophone, you haven't developed the embouchure muscles yet to keep the sound consistent and steady with a harder reed.

As another point to think about … different reeds brands are not consistent with each other. For example, a 3 rico orange box (the bottom of the barrel in my opinion), is softer (and less consistant) than a 3 rico blue box. So if you are a beginner, orange box or blue box rico's are a good place to start, because it's not going to make a big difference to your sound at that level as you have no control yet. But as you develope, it is a good idea to think about investing better reeds (often more expensive) check a reed comparison chart to find a reed that is close to what you would normally buy from your old brand.—> Rico Jazz Select, Vandorens (there's a ton of them, experiment), La Voz, etc.

There's also differences in the cut of the reed in how it affects your sound. Rico Jazz Select's for example offer filed and unfiled. Unfiled creates a darker, less refined sound and then filed creates a brighter, more commercial sound - niether is better or worse, just different… it all depends on what you want to go for.

Another important thing is to learn how to "break-in" reeds so they can last long for you. I haven't got into this a whole lot, but I'm sure there's TONS of stuff on it if you "google" it. Also, invest in a reed storage device of some kind. (one of those clamp down lunch containers from the store, the vandoren blue case that holds 4 reeds is good, Rico makes some good storage devices. These will keep your reeds moist, and in turn they will be easier to play and last longer.

I hope this helps!

Happy Playing!
References :
Me - I am a 2nd year in a contemporary music degree program student - majoring on saxophone (and doubles)

Those numbers indicate the number of strength a certain reed has. the higher the number (3.5, 4, 4.5, 5), the higher the strength. The lower the number (2.5, 2, 1.5, 1), the weaker the strength. Usually weak reeds tend to break kind of easily. Stronger reeds are usually harder to break than weak ones. The stronger the reed though, I think I've heard that it makes your instrument lower in tone. Weak reeds tend to make a pitch higher in tone. My best guess here.
References :
3 Year Alto Saxophone Player
1 Year Tenor Saxophone Player

Start on a 2 or 2 1/2….if your playing primarily jazz go on the lower end. Reeds don't directly affect your sound but the harder the reed the harder you have to blow and your embouchure changes so your sound does too. Once you get to the point you can unwrap a reed and play on it without soaking it first for too long…you need to move up another half size right away.
Also some mouthpieces work better with different sizes of reeds…but as a beginner you dont need to get into that. Ask your band dirctor if you have any issues or questions.
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Don't always trust what the sales people tell you because many don't know the difference themselves especially how it affects the tone.

I'll try to lay it out as simple as possible.

1) The number represents the strength (how stiff it is or how bendable it is). The higher the number, the higher the strength.

2) There are many different numbers (strengths) because mouthpieces vary widely in their tip openings (the distance from the tip to the reed).

3) You need to match the tip opening to the number (strength) that creates the best sound and playability for you.

How it affects the saxophone?

Example 1: If you find that your sound is very stuffy or difficult to blow (too much resistance) then your reed is probably to hard and you need to move to a lower number.

Example 2: If you find that you have difficulty playing higher notes in tune (they are too flat) or your sound just cuts off then you probably need to move to higher number.

Which brand to choose?

That's a personal choice. Each brand has a bit of tonal variation in the sound. One brand's strength is not necessarily the same as another. So a little experimenting is needed.

There is no beginner strength or professional strength. The mouthpiece determines that. Michael Brecker played on a 2.5 La Voz reed on a fairly open mouthpiece, so did Benny Goodman.

Hope that helped
References :
Professional musician, Saxophone Teacher.