From the informations you have given us, I will try to give you solid advice. Please be kind if my assumptions are wrong.
In the near future I intend got get rid of my Microsoft XP and the CMS "WebtoDate". So I need a suitable alternative for CMS.
Web2Date is a simple CMS with very limited functions designed with the unexperienced user in mind. It was probably the right tool for your task. Typo3 might be a CMS too - but that's all those two programs might have in common. If Web2Date would be a ... let's say ... mountain bike, then typo3 would be a Boeing 747. It's optimized for huge websites with thousands of pages, administered by editorial teams with a dozen or hundreds of members. The administrator should ideally be a professional computer admin or at least a very dedicated enthusiast.
To me it seems to be very complicated to get installed Typo3 and the whole LAMP environment.
If you feel uncomfortable with installing a LAMP environment you shouldn't even try typo3. You won't get anything
done. Believe me, I've tried and I had no trouble installing and configuring the LAMP environment. And I attended courses in typo3 management. All those lessons gave me an idea what would be possible with typo3 but after hours of practice I never got further than setting up a simple website.
As a side note: The typo3 team split up recently and is now following different courses. Atm nobody really knows where typo3 will end up. It might be a sinking ship.
"WebtoDate" is doing its work only in my system and without any help by an external server. The new CMS should be able to do exactly the same procedure.
This doesn't sound like you even need typo3. There are a lot of tools which are certainly better equipped to get your work done. If you really want a professionally sized CMS you should consider Joomla.
But it would be even better if you described what exactly you used Web2Date for and what exactly you want to get done in the future. I'm sure somebody here could name you very good alternatives that probably don't require LAMP and that certainly don't have the steep learning curve that typo3 has.