It looks like the original logos have an emboss filter applied to give a 3D or raised effect. I use Paint Shop Pro and have a group of filters from Graphics Plus. It contains an Emboss filter that you use sliders to control the effect. I think the Gimp can use Photoshop compatible filters, as does PSP. Here's a link to a page with dozens of filters, also called plug-ins.
Magstags Filters Page
Older versions of Paint Shop Pro included Animation Shop. It is now a separate program. This program is easy to use to make GIF animations. I've made animations from NBA Live screenshots.
PSP9 includes Animation Shop 3. Here's a 30 day trial.
Download Animation Shop 3.05 Free Trial - Animation Shop provides the tools you need to easily add animated buttons, banners and other cool effects to your web site - Softpedia
I believe this is a legal download for PSP7 trial. At that time the trial did not expire. I have also read that there was a free and legal download of AS available but I could not find it.
Download Paint Shop Pro with Animation Shop v7.0 Shareware software - Softlookup Downloads