Different strings can change the sound of a mandolin dramatically. I found this out the hard way, the first time I changed the strings on my A-Style mandolin. I did not use the same brand that had been put on it by the manufacturer and, when I played the new strings, I found that the sound of my mandolin had changed completely. I called the manufacturer in tears because I thought I had ruined my mandolin, and fortunately, they knew what strings had been on it originally because they use only one brand on their new models. So I bought a new set of those strings, put them on my mandolin, and everything was fine.
The point here is that there are really no "good" strings, or "bad" strings – it's simply a matter of which strings produce the sound and playing action that you like. The strings that I had put on my A-Style mandolin were a very popular brand, but I hated the way that they sounded. So I gave them to a fellow mandolin player who loved them, and now that's the only brand he buys.
You can begin to personalize your mandolin by choosing the strings that sound best to you, and there is really no way to do that other than by buying them and putting them on your mandolin. Most guitar stores sell mandolin strings in sets of eight (two of each string). You should change all of the strings at the same time unless you are just replacing one broken string. The acoustic music stores also sell complete sets, but you are more likely to find individual strings for sale there as well. As you become a more experienced musician, you may find yourself becoming more and more particular about your strings. It’s very common for experienced musicians to 'split' sets – meaning that they'll use the "A" strings from one set, and the "D" strings from a completely different set. Rather than buying two complete sets and using half the strings in each, they buy only the individual strings that they prefer – assuming, of course, that the store will sell them individually.
Since they can make such a huge difference in the sound, I suggest you ask what strings are on your mandolin, at the time you buy it. The seller may not know, especially if you are buying over the internet, but it is always a worthwhile question to ask. Write that information down and put it in your mandolin case. When the time comes to change your strings, buy a different set and try them out. I leave the empty string package right in my mandolin case, so that I know what's on there at any given time, and keep a list of strings that I've tried, that I didn't like and quickly donated to other player, so that I don't buy them again. I do keep one set of strings that are "not bad, but not the best" – these are for emergency use in case I break a string on my good set.
Because most manufacturers sell multiple sets of strings, knowing that you have "D'Addario strings", or "GHS strings" isn't enough information to make sure that you get the exact same strings you're used to. If you want the exact same strings, then you also need to know the composition and gauges of what you have now. If you look at a package of strings, you'll see that it identifies 1) the manufacturer, 2) the string composition – such as "steel", "bronze", etc., and 3) the string gauge - usually identified by numbers, like E-11, A-16, D-24 and G-38. A different set by the same manufacturer may have different numbers, like E-09, A-13, D-20, and G-32. Those numbers refer to the thickness (gauge) of the strings.
The string composition determines the timbre. Strings made of bronze are considered brightest type of acoustic strings. Phosphor Bronze is less brilliant, and a little richer. Stainless steel, silver plated copper, nickel/iron, nickel plated steel and nickel produce a heavier bass sound. Gauges affect the tension at which a string vibrates to achieve the desired pitch. A light string (lower number) is more flexible and vibrates fast with a bright tone, but sustains less than a heavier string (higher number). If you compare two different sets of strings made by the same manufacturer, you'll see that even though both packages contain 2 of each mandolin string, the gauges and composition (and therefore the sound) are very different. Experienced players purchase the composition and gauge of string that produce the sound they prefer.
Some musicians can only use stainless steel strings. This is because their hands sweat when they play, and the sweat causes strings of other compositions, to quickly rust.
You can also buy flat wound strings, which look and feel quite different than a normal string. Most strings have a metal core which wrapped with another string, and you can feel (and hear) the ridges from that wrapping when you move your fingers along the string. This wrapping is minimized on a flat wound string, so they sound richer, produce very little string noise, and are easier on your fingers to play. As can be expected, they're a lot more expensive than normal strings, but may be a worthwhile purchase if you feel that your fingertips hurt too much after you practice.
The best thing to do is experiment with different manufacturers, composition and gauges of your strings, and use the ones you like the best.