Is there any reason to hoard gems/runes?

As for runes, you should focus on runewords useful for your class - see Runewords list. You can upgrade low level runes into higher level ones. Some high level runes are useful even without runewords - for example, Ohm (+50% Damage) and Zod (item become indestructible). So you should be interested in keeping all runes you found to upgrade them eventually.

As for perfect gems, I personally use them to reroll charms - there is recipe any 3 perfect gems/skulls + magic item = random magic item of same type and it requires lots of gems to roll good charms - I personally try to roll +X all resistances small charms and +1 skill grand charms. Having good charms helps a lot on Hell difficulty. You can see list of all possible charms suffixes/prefixes here.

As for inventory management, I can recommend GoMule:

This is a muling application for the computer game "Diablo 2" which allows items to be stored and transferred between Single Player characters outside of the game. The goals of GoMule are to:

• Easily transfer items between Diablo 2 character files (d2s files) Give infinite storage capabilities of both items and gold through the use of stashes (d2x files)
• Allow users to easily locate and sort items in their stashes
• Speed up common muling processes, through multiple pickup and drops
• Allow Unix systems to easily mule their items

Although GoMule does edit the Diablo 2 game files, it cannot be considered a character or item 'editor'. There are very strict restrictions on what you can edit, GoMule will never support stat, skill or item property editing.

It is software that allows you to create separate file on your disk to store your stuff. It works with save files, but never touches game files. It also automatically creates your save backups every time you attempt to change something, so you won't lose your char if something goes wrong.

If you are concerned about duping - every item has unique id, and GoMule has 'remove duplicates' option to clean them from your characters/stash.

Starting with gems, as you can probably guess from the lvl requirement, even perfect only requires 18. They are not for end game equips, keep enough to upgrade your runes and you are okay, alternatively you can use them to boost areas of weakness before you get good equips that does more. I wouldn't keep more than 4 perfect even of those I usually use. Those for upgrading runes should take priority.

Occasionally, somewhat decent magic/rare loots may come with small number of sockets(up to 2 for rare and 4 for magic) which basically allows you to customise the remaining part of that item. Percentage effect from gems can be useful even till later into the game. Though runes often perform better in most situations.

As for reasons to keep runes...

This is the effects of the highest level runeword "Breath of the Dying":

50% Chance To Cast Level 20 Poison Nova When You Kill An Enemy

Indestructible

+60% Increased Attack Speed

+350-400% Enhanced Damage (varies)

-25% Target Defense

+50 To Attack Rating

+200% Damage To Undead

+50 To Attack Rating Against Undead

7% Mana Stolen Per Hit

12-15% Life Stolen Per Hit (varies)

Prevent Monster Heal

+30 To All Attributes

+1 To Light Radius

Requirements -20%

It requires 6 socket and therefore not applicable to all weapons but on weapons that can have it... I don't exactly get items from the floor better than this everyday.

More commonly there is "Enigma":

+2 To All Skills

+45% Faster Run/Walk

+1 To Teleport

+750-775 Defense (Varies)

+(0.75*Clvl) To Strength (Based On Character Level)

Increase Maximum Life 5%

Damage Reduced By 8%

+14 Life After Each Kill

15% Damage Taken Goes To Mana

(1*Clvl)% Better Chance of Getting Magic Items (Based On Character Level)

It only requires 3 socket so basically any armour can potentially have this effect. It is versatile and far better than most floor loots so I really suggest reserving some space to get these effects.

A list of runewords can be gotten from the Diablo wiki