What is the best procedure to update from Leopard (or Snow Leopard) to Mavericks?

Question

The pacient:
Macbook Pro A1278
Running 10.5.8 -- but have an Update DVD to 10.6 (Snow Leopard)
Got slower in start-up
Very slow in power-off (takes lot of time on shut-down!)
What is the BEST procedure to update it from Leopard to Mavericks?
A) update & clean
Backup to Time Machine (in Leopard)
Update from 10.5.8 to 10.6 (Snow Leopard)
Update 10.6 to 10.6.8
Donwnload and Update to Maverics
Do any kind of clean to increase speed in start-up / shut-down - Any suggestions?
or
B) fresh install & update & recover Time Machine
Backup to Time Machine
Reinstall a fresh 10.5.8 (Leopard) - should increase speed in start-up / shut-down ??
Update from 10.5.8 to 10.6 (Snow Leopard)
Update 10.6 to 10.6.8
Donwnload and Update to Maverics
Recover users data & config from Time Machine
I am thrilled to heard your advices!!
PS. Aditional suggestions to make a faster boot / power-down , before or after updating are very welcome ;!)

Answer 1

Go to  Menu > About this Mac > and tell us Version, Processor & Memory specs on your Mac. Also available hard disk space, by choosing your Macintosh HD and "Get Info" (cmd-i)
If you're having issues now with slow sratup and shutdown, it's probably a third party item. If it is, then it may limited to your user account. If that's the case and you do a clean install, then migrate you will wind up migrating it right back.
The first thing to check would be to boot into your Guest account and test, or try starting in Safe Mode and see if the problem still occurs?
Restart holding the "shift" key.
(Expect it to take longer to start this way because it runs a directory check first.)
If this works look in System Preferences > Users & Groups > Login items and delete any third party login items.
Also look in /Library/Startup Items. Nothing is put in that folder by default, so anything in there is yours. Then log out and back in or restart and test.
If the problem is sorted, be sure to make a new backup before proceeding. Since the problem is sorted and you have a backup without the offending items, then there's no reason not to use the simple upgrade method you outlined in A. With the exception of "cleaning". The only cleaning your Mac should need is with a soft cloth. Stay away from so-called cleaning/optomizing utilities.