While you are at it, put an apprentice or journeyman set of alchemy apparati in the Arch Mage's room.
IMO, a good sword to put in White Stallion lodge would be an Ancient Akiviri Katana since a lot of people may not start the main quest until later when better swords are available. It is light-weight (18.00) and powerful (15) for early levels, and would be good to enchant. A fine steel longsword is heavy and already available in Chorral sitting next to a silver shortsword, so there is not much point.
I don't know if you could afford to recharge your mega-super-sword.
What do you want to kill, when do you want to kill it, what difficulty level are you playing, and what is your blade skill going to be?
Here are several considerations.
1) An Honorblade-type sword will be too heavy (44.00) to carry around and swing during early levels, and it will be obsolete at level 20 when daedric longswords show up. Honorblade and Umbra kick butt because they are weightless and effective against ghosts. If you can put in a weightless sword that can be enchanted, it would be nice. When playing weak races, I like to cheat by using permanent bound maces.
2) An enchanted blade in the hands of a blade novice drasticaly lowers the base damage and the sneak bonus, so a big sword to enchant might be wasted.
3) A sword with powerful enchantments early in the game will be difficult to recharge with petty/lesser souls without Azura's star. And, you can get into trouble with soul trap on a weapon when you are carrying around black soul gems and rare grand soul gems when everything trying to kill you has a lesser or petty soul.
4) Early on, most of your killing will be skeletons, men, wolves, etc at 20 hp each, so big damage is wasted.
5) At upper levels, you have the problem of leveled monsters that have over a thousand hit points, but only contain grand souls. You have to weigh power lost to power gained for recharge (1600 for a grand soul).
6) What do you consider breaking the game (1 hit, 2 hits, 3 hits, 10 hits?)
Drain Health 100, Fire 9, Shock 9, Frost 4 (20 charges from a greater soul gem) is a maximally cost effective sword to use against big monsters until Will-o-the Whisps show up at lvl 11. Then it starts to have some trouble due to a light blade and low charges. It is too expensive to use against the everyday rif raf at starting levels unless you have Azura's star. It is light-weight with a silver shortsword. Steel longswords are heavy and their extra damage is fairly insignificant when enchanted. The sword kills zombies in one strike and the formulation takes into consideration the fire weakness of zombies, the fire resistance of Flame Atronachs, and the frost resistance of Undead for the best compromise. You could boost the numbers, but cost of damage increases as you add more units.
For upper levels, fire is the best element for the following reasons: Storm Atros are the toughest non-leveled things out there, so what kills them kills all the rest of the non leveled monsters in the same number of hits or less. They are resistant to shock 100%. Undead are common among the leveled monsters and they are highly resistant to frost but weak to fire. Other leveled monsters (Ogres, minotaur lords, goblin warlords etc) are average in regard to elements, so fire does just as well as shock and frost. Once you have enough fire to kill a Storm Atros, you can start adding Shock to the budget for the leveled guys.
I'll assume that you want the most damage for the least amount of recharge, which means killing in the fewest, cheapest strikes.
You already know this but for those who don't...
The most efficient way to kill, especialy at mid levels, is with Drain Health plus Weakness to Magic. The drawback is that there is a time constraint. The Drain Health stacks based on the number of strikes within the time limit of the weakness, so the first hit does 100 damage, the second does 200, the third does 400, etc. The damage is not permanent. If it does not kill, it dissipates immediately.
If you want to kill in a set number of strikes, you have to add other damages, such as weapon base damage and/or elemental damage. For instance, this sword can kill all non-leveled monsters in two strikes. The toughest customer is a Storm Atronach at 350 hp.
With a grand soul gem capping it at 85 magic units, you have 18 charges Soul trap 1s Drain Health 100-1s Fire 14 Weakness to fire 100-1s Weakness to Magic 99-3s
Two strikes does 200 drain health damage (on the second strike), so you need 150 points of damage from other sources. Fire = 14+ 55 = 69, so the sword base needs to do 81more. That could be 6x12 + 12 from base damage by way of a single sneak strike and followup hit. Without the sneak attack, it takes three strikes (the stacked Drain Health then does all the work). Efficiency w/ sneak = nine Storm Atros per grand soul gem recharge, w/o sneak = six.
Almost eqivalent are the following swords made with a grand soul gem.
Soul trap 1s Fire 31 Weakness to Fire 100-1s Weakness to Magic 100-2s
Soul trap 1s Fire 21 Shock 14 Weakness to Fire 100-1s Weakness to Shock 100-1s Weakness to Magic 100-2s
All three (and similar) can kill a storm atronach in 3-4 hits, and a lvl 54 goblin warlord in 7-8 hits when using a daedric longsword. The elemental swords will not do a two hit sneak kill, but their damage is permanent, which is good when you are getting pounded.
Although a minimum of 7-8 strikes are needed to kill a goblin warlord (30 x lvl 54 = 1620 hp), often a dozen or more hits are needed because of blocking, paralyzing knock downs, and armor. That means recharging after every kill, and sometimes during a fight. A fight needing only a dozen hits to kill is not a big deal unless you run out of charges so adding that would be my first consideration. Assuming that you are restricted to the power to cost ratio of the enchanting alters, adding more damage to the sword also uses more power per hit, so you probably can't afford to use a One Hit Wonder late in teh game. With no restrictions on the sword build I might add more elemental damage to the equivalent of 90-95 up from 85 on the enchanting alter scale but it might be a case of diminishing returns in regard to saving hits via more damage dealt.
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