I quite new to discworld too. The books can be read out of order, although sometimes have references to previous books which can be mildly confusing. Its probably best to read them in order, although, as Stephen F. Wilkins said, the first two books can be quite dull.
I think the series is best read in order. Can't for the life of me understand why the first two books are apparentely so disliked. TCOM had me hooked right from the first page. The first two ease you into the Discworld gently. Admittedly there is very little plot in them but when you're laughing as hard as you will be does it really matter?
If you don't want to start with them then do Equal Rites first. The character of Granny Weatherwax is nothing like she is in later books but it's still a good read and is the first book in the series when you begin to get an impression of how vast the world Pratchett has created really is.
Alternatively you can do them in sub-series. The main groups are Rincewind and the wizards, night watch, witches of Lancre, Death Susan and the Auditors of reality and the standalones. There are two Moist Von Lipwig books as well now.
The best series of novels is generally agreed to be the ones centred on the night watch. To get the most out of them they MUST be read in order. Therefore you will need Guards, Guards, Men at Arms, Feet of Clay, Jingo, The Fifth Elephant, Night Watch and Thud.
All of the books mentioned above are great. If you read them in order you will see how the mainj character evolves over time. Reading Thud before Guards, Guards would not be a good idea.
I don't know that I'd bother. I know people who have got really into TP, but I just don't see the attraction after reading 6 or 7 of them - they have always said "Oh, you should read "xyz", "abc" is not that great", but I've just been increasingly disappointed. All are mildly amusing, but at the same time shallow, repetitive, formulaic, predictable, unsubtle, condescending, undemanding and about as prolific and exciting as a Windows security patch.
The first two books (and the later books featuring Rincewind) are very funny but really just a series of gags with a very minimal linking plot - very much The Hitch-Hiker's Guide to the Discworld. Pratchett's real gift is that he can turn out a genre parody in which you actually care about the plot and characters - which only starts to emerge around book 3 & 4 (Equal Rites, Mort).
So, by all means start at the beginning, but if "Colour of Magic" doesn't float your boat give it another chance with "Mort".
First book I read was the monsters regiment, which is one of his later books. From that I went back to the start, but didnt enjoy them as much as his later works. Dont be put off by some books being classified as childrens books (the wee free men) they are still worth the read.
I've experimented on friends and found Guards! Guards! to be a great introductory point. Then revert as quickly as possible to the correct sequence - you will love some and merely enjoy the others. Most important as a beginner is finishing one book to get used to his style. Don't give up if the first one you read is dissappointing. Read 4 or 5 and you won't look back.