Well you could always install FSO - the open source Freespace engine which fixes all of those issues and lets you play in really nice graphics. FS1 can be played through by the FSport mod for FS2.

Links abound for how-to's on installing Freespace 2 FSO:(http://www.gog.com/en/forum/freespace_series/quick_and_simple_freespace_2_scp_installation_guide)

automated installer + instructions:
http://www.hard-light.net/wiki/index.php/FreeSpace_Open_Installer

However, if you want the retro feel, this thread has the fix for you:

http://www.gog.com/en/forum/freespace_series/fix_for_unreadable_fonts_on_freespace_2

A forumer confirmed this fix works on both vanilla FS2 and FS1, so hopefully it will work for you! (If you don't go the Freespace Open route of course :P)

Found a page where the user can manually modify the registry. The same way the mod launcher seems to.

In case you want to play both 1 & 2 without mods first.

In the registry find this path:

Local Machine
Software
Volition
Freespace (1 or 2

No in the the Freespace(or 2) directory. Right click in the right pane.

Choose new-->DWORD

Write this:
D3DTextureDivider
Then right click it and change the zero (0). To 1

Now do that same thing for the rest as I list them below:

D3DUseLargeTextures
D3DTextureOrigin
D3DLineOffset


These settings will do several things. They will correct the text in game. Which will still look like crap. But it is fixed. It will show the stars when flying around that disappeared. It will use better textures for FS1.

So hope this helps. It works in my FS1 game from GOG =D