Yes this should be sufficient. Lowercase plus numeric (the output of sha1) gives you a search space of 36 characters. At 40 total characters in a SHA-1 hash, the search space is 1.84 x 10^62. If you take a relatively strong password (upper case, lower case, numeric and specials) of length 8, your search space is 6.70 x 10^15. However, many sites require the use of mixed case and or a special/numeric added so you should probably sneak those in someplace to cover sites that require such input. Also, many sites also limit password length though if you truncate the hash and stick with the maximum allowable password you should be better than the avg user.
You can use GRC Haystack to run some calculations on how quick you can break a password. At a trillion guesses a second the above 8 character example falls in about 1.12 minutes vs 5.84 hundred trillion trillion trillion centuries for your hash.
1) I'd make sure your master password is not a dictionary word or words, contains upper/lower/numeric/special and is completely random. Then add in the website and hash the entire thing. As long as the algorithm is unknown cracking is theoretically impossible.
2) Consider moving to SHA-256 as well as SHA-1 is flawed.
3) Take the 40 character output and use it to create a mixed case + numeric + special password that fits in say 13-15 characters (most sites will fall in this range of max length). It doesn't have to be fancy, i.e. if a numeric pops up then the next alpha is uppercase, if there is a number then insert a special in after it (e.g. if '1' pops up inser a ')', if '2' pops up insert '(')