SQL Server 2000 Backup + Restore Question

Of course I'll try this before I go live, but I figured I'd ask
here first. I've read the docs, and the answer is unclear.

My current backup strategy is:

Take a full database backup occasionally (like, every two weeks).
Back up logs every five minutes.

This works, but restoring the database all the way through can
take a while, as I've sometimes spun through 800+ log restores.

I'd like to change to

Take a full database backup occasionally (like, every two weeks).
Take a differential backup every day.
Back up logs every five minutes.

So, I'd have this set of backups after day two

FULL
LOGS 1-100
DIFFERENTIAL
LOGS 101-200

When I go to restore, do I always have to do
FULL
DIFFERENTIAL
LOGS 101-200

or can I do

FULL
LOGS 1-100
LOGS 101-200?

I guess what I'm really asking is: is there any reason to keep
the "old" logs around (in this case 1-100), if I assume I always
have the latest differential?

I suppose I *might* need them to do a "point in time" restore,
i.e.
FULL
LOGS 1-53.

but assuming I never want to do that, can I discard the logs
that are earlier than my latest differential?