You can also add sequels to games which were published on Amiga but the sequels were not (if you liked the precursors of course).
Maybe even start with those to feel a bit more connected to the games.
Coming to mind:
- Settlers II: very similar to Settlers, a bit more complex, several improvements, missing the split screen two-player mode though. There is a modern remake but I highly suggest playing the original version.
- Syndicate Wars: same spirit as Syndicate but quite some differences in terms of gameplay. A favourite of mine.
- The Worms series.
- Theme Hospital: like Theme Park but you have to manage an hospital (with some silly diseases etc...) (edit: ah, Nostalgeek had already mentioned it)
- Dune 2000 (more or less updated version of Dune II, using the same engine as Command & Conquer/Red Alert and therefore can be a good introduction to the gameplay of this series) and Emperor: Battle for Dune (this time it is in 3D)
- Super Cars International: http://eab.abime.net/showthread.php?t=26575
Which leads to the remakes (should work on your PC):
. made by jotd:
. of Lionheart:
. clones of Turrican:
There are also games you should give a try to feel a specific experience.
For instance, at least one game of the Descent series you should try. It is a FPS in which you pilot a ship and can actually move 360° (i.e. completely rotate in every direction) and for instance you can fly "upside down", laterally etc...