I have noticed that many bitcoin addresses begin with numbers or uppercase characters. I realize that all addresses begin with the number one but can I generate an address with the second character being lowercase? Is it significantly harder to generate an address with multiple lowercase letters at the beginning? Are there any other limitations in regards to generating vanity addresses?
Overall, you have to start with a "1" (unless you're doing alt-coins). Then the first letter is the only one that can be more tricky to generate (some letters from the end of the Base58 alphabet are harder). Also, generating an address with a lot of leading 1s is a lot harder than any other characters due to how addresses are constructed (leading 1s mean that you have a whole leading byte of 0x00 at the start of the address, or about 1 in 255 change in comparison to 1 in 58 chance for any other letter). After the leading 1s and the first letter, everything else is the same 1 in 58 chance of being any letter no matter what it is.
So all in all, you can generate any combination of letters and numbers in a Bitcoin address as long as it starts with "1", but some combinations are harder to generate. The same can't be said for other altcoins with a specific netbyte, since some starting patterns may be outside of their name space.