GD is shipped with PHP, it's why it's always an option. ImageMagick is a 3rd party system binary (it has to be installed on the server). Commonly the paths to IM are:
/usr/bin/convert
/usr/bin/mogrify
If you have SSH access you can just try:
which convert
which mogrify
If they're installed then it'll tell you the paths, if it isn't installed it'll tell you.
Found convert binary:
[root@server ~]# which convert
/usr/bin/convert
No convert binary:
[root@server ~]# which convert
/usr/bin/which: no convert in (/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin:/root/bin)
As for dimensions, I use 200px for thumbnails, you can too.