1. You need to use the original disks for that model of Mac or a retail package newer than it.
2. Macs which shipped without an optical drive either use an USB thumbdrive or have a preloaded recovery partition.
3. If you use the same Apple ID, your past Mac App Store purchases will be freely available. Snow Leopard is a DVD install and not available from the Mac App Store.
An example: your brother and you have got different Macs that came with Mac OS X Leopard. In this case, the Mac OS X DVDs that came with your Mac include a special Mac OS X version only compatible with your Mac, and the same for your brother. In this case, you won't be able to use your brother's DVD to install Mac OS X, because the version that they include isn't compatible with your Mac.
Then, Niel mention retail packages. In that case, you can use that DVD to reinstall Mac OS X on your Mac, always that it includes a newer Mac OS X version than the one that came with your computer.
If you have a Snow Leopard DVD, use it to reinstall Mac OS X onto the new SSD instead of the DVD that came with your Mac, so you will save time and headaches. If not, you can use your brother's DVDs but only if it contains a newer Mac OS X version (for example, Snow Leopard) or he has got the same computer with the same model as you