I'm first to Linux. I hosted Linux server which runs as virtual machine (AFAIK) at $30 for one month.
What, just to get used to Linux ?? As Zvoni said, please look at Virtual Box, any linux you want, a GUI and would cost you nothing.
- Can I run a GUI interface on the server side? If not, how can I use Internet, e.g. for download Lazarus?
Possibly, but probably not very well. From memory (a long time ago) the same place you got putty from also has an xserver ? Don't be fooled by the term xserver, its something you run on your desktop that connects to the remote server. The remote server does something called
X11 forwarding and the X gui display appears on your desktop's window. Does require a very fast connection to be usable. Its most likely the remote server will not allow you to do so for security/bandwidth reasons.
There are other tools as well but they are not built in and, again, unlikely to be available.
- Are there any remote connection tool to use from Windows client (GUI would be better) other than PuTTY?
Probably not. Honestly, if you wish to become a power Linux user, you do need to come to terms with the command line.
So, getting back to Zvoni's answer, Virtual Box, its free, it runs on Windows (I believe) you can install any linux distro you like (and they are also free) and you get your GUI, much faster response, no security worries.
A typical linux install in a VM (Virtual Machine) needs about 20G disk space, if you can give it it two CPUs (but one will work). To install a linux distro, download a .iso file from the distro's download page, eg my favourite,
https://cdimage.debian.org/debian-cd/current-live/amd64/iso-hybrid/debian-live-12.7.0-amd64-mate.iso Its 3Gig and is easy to use, light on resources.
Davo