There is no difference between Panther disks re: upgrade.
The black-boxed version will upgrade or do a clean fresh install, whichever you prefer it's all the same price.
It shoud contain 4 disks 3 x black ones (numbered) & 1 x white & blue one for X-code tools
And yes, you can go straight fom 10.1.5 to 10.3...
Download the combo updater to 10.3.4 from Apple first, do your install of Panther, run the updater and you're sorted.
You will notice the difference, believe me.
Personally, I haven't gone to 10.3.5 as I've heard of some teething probs but that's your choice. 10.3.4 seems OK to me...
Yes, you may have to delete some things/back them up but the Panther disks look at your HD and tell you how much space it needs to install.
If space is at a premium, then don't install all the languages and printer descriptions.
Expose should run OK on a G3, maybe a little jerkily but that's just a wild uninformed guess.
Also, the best investment for you would be to buy David Pogue's: Panther -- The Missng Manual. It's really user-friendly, covers all the apps that come with Panther and is worth every penny.