I think it would be wise to first link the two main Apps used ~ The first is RyanZA's
z4root which is probably the most simple way of rooting your SGS.
With z4root it's as easy as downloading the Ap, installing on your phone and running it. No need for any additional third-party software (Odin) or a PC.
The next Ap and probably the first after rooting is to perform a LagFix.
Again we see RyanZA coming to the rescue with his App
RyanZA OCLF
Again, like z4root we have another Ap that is downloaded direct to the phone and run on the phone. As above, no Odin or a PC is required.
_wolf_ has already mentioned Titanium Backup so I'll leave that one but suffice to say that would be my next.
So, to continue I'll add just a couple of others more for the time being:-
1.
SetCPU for Root Users ~ SetCPU changes the CPU settings
(capable of overclock and underclock) on a rooted SGS and many other phones.
Note: Galaxy S devices: use conservative scaling.
2.
Root Explorer (File Manager) ~ Named as the ultimate File Manager.
Access the whole of android's file system
(including the elusive data folder!).
SQLite database viewer, Text Editor, create/extract zips, multi-select, execute scripts, search, remount, permissions, bookmarks, email, thumbnails, APK binary XML viewer.
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Okay, there's my initial catch to start you off.
Must dash... Due back in surgery.
Beards