The purpose of this guide is to offer some perspective to any interested parties on good, common, and generally "safe" heirloom choices in each item class as well as some explanation as to why those choices are better than others in their same class. When pertinent, heirloom choices that should generally be avoided will also be mentioned.
Disclaimer: The most important factor when deciding on an item to heirloom should be whether you are comfortable moving in it/attacking with it. This guide is meant to be an informative rather than authoritative one with respect to that point, as there are many players who are surpassingly effective in combat with very unorthodox equipment choices. Your gameplay experience may also lead you to a different conclusion about specific items those that I have reached here. At the end of the day, you should use what you're good with and can afford, regardless of what this guide says or does not say about it.
Horses
General info about heirlooming horses: Some new players make the mistake of heirlooming a horse first, only to find that playing cavalry in cRPG is a very different experience than playing it in native. Make sure you've either spent a generation or more as cavalry or a sufficient amount of time testing it out on a skip the fun character before you commit resources to being cavalry, or you will likely end up selling your +1 horse back at a loss. Keep in mind also that horses are very expensive. Heirlooming a horse that is more expensive than what you need to function and that you cannot use all the time due to cost is less advisable than heirlooming a cheaper but still effective horse that you can use constantly or almost constantly and still make money.
Good heirloom choices:
Destrier - Possibly the best horse overall. A Champion Destrier offers good durability, speed, and manueverability at a very competitive price.
Arabian - The most manuverable horse and the other main contender for the title of best horse. It is most commonly favored by horse crossbow and 2h cavalry players but is great for virtually all other types of cavalry as well--if they can meet the rather steep requirements to ride it.
Rouncey - A favorite of cavalry players on a budget and some hybrids. A Champion Rouncey is slower than a Champion Courser but has comparable stats in most other areas and is significantly cheaper and easier to ride.
Situational heirloom choices:
Courser - The fastest horse. It is the premier horse for lancing due to its speed but other types of cavalry may or may not be better served by some of the other choices available. Note that if you want to ride a heirloomed Courser, you may want to trade for one as opposed to actually spending points on one, as they are very common on the marketplace.
Bad heirloom choices:
Plated Charger - Despite the fact that it has 70 listed armor, this, like all other horses, only applies to its body and head. It effectively has zero armor when people aim for its legs, which is comparatively easy for anyone who is aware of you thanks to how slow the Plated Charger is. Compounding these issues is its tremendous upkeep cost (over 4000 gold per repair) and how it sits very high off the ground--1h and 2h cavalry players riding a Champion Plated Charger will have to be better at aiming their swings if they want to connect with an opponent compared to if they rode a smaller armored horse like a Cataphract.
One-handed
General info about heirlooming one-handed weapons: For one-handed weapons, more than for other weapon types, you will need to be willing to determine what you value most and make some compromises. As a rule of thumb, the most damaging one-handed weapons are very short, which are harder to use in most situations and make you very easy to kick if you are not careful, while the longer one-handed weapons may be comparatively lacking in damage against targets with 50 or more armor depending your build.
Good heirloom choices:
Italian Sword/Knightly Arming Sword/Nordic Champion's Sword - Very well-balanced weapons that are variations on the same theme of "classic cruciform sword". The Italian is the fastest, cheapest to upkeep, and has the best thrust, while the Nordic Champion's Sword and Knightly Arming Swords are slightly longer and have slightly better slashes. All three of them have great reach for a 1h and give you good attacks in all four directions.
Warhammer/Steel Pick - Your go-to weapons if you want to take apart well-armored targets. The pick is a little faster and has moderately better damage against the most highly protected players, but the warhammer has knockdown--a very good chance of it too.
Broad 1h Battleaxe - There are many different offerings when it comes to 1h axes, and this is arguably the best of them all. The Broad 1h Battleaxe is fast, powerful, and shreds through shields like they're cardboard/SCA props. Furthermore, although it is a shorter weapon, as all axes are, it does not absolutely cripple your reach in the way that the shortest weapons do. Keep in mind also that despite the fact that the secondary mode on it has a decent amount of piercing (28p after three improvements), it's mainly there for flavor; the raw power of the primary mode will pretty much always be better damage.
Situational heirloom choices:
Military Cleaver - This is possibly the one exception to the above rule about damage vs. ease of use. A Masterwork Military Cleaver does as much damage as an unheirloomed German Greatsword (38c) and has a very respectable 92 length, at the expense of being on the slow side for a 1h and not having a thrust. The fact that it is quite cheap for what it brings to the table is also a good point.
Long Espada Eslavona - A favorite of some swashbucklers. It's very long, very fast, and has a very mean thrust (31p!). Its heirloom bonuses are also better than most other melee weapons, but this is likely a consequence of its base form being rather weak for its cost. Note that if you want to wield a heirloomed Long Espada, you may want to trade for one as opposed to actually spending points on one, as they are very common on the marketplace.
Bad heirloom choices:
Side Sword - A long time ago, this apparently used to be the best 1h sword hands down. Those days are long past, however. The Side Sword in its current incarnation is statistically identical to the Long Espada except for a slight increase in speed and a slight loss of range. It's also a little cheaper. That said, it's not really worth heirlooming, considering length and damage are at a premium for 1h. While you may have to sacrifice one for the other, you probably should not sacrifice both for small gains in other areas where 1h already has advantages, such as speed or cost. Unfortunately, this is what the Side Sword ultimately does.
Espada Eslavona - A sword that has the dubious distinction of being the weakest weapon in the upper price point of 1h. The younger brother of the Long Espada has an even stronger thrust at the expense of range and damage; on a Masterwork Espada Eslavona, you get a 33p thrust in exchange for 90 length and 28c on your slashes. The result is a Masterwork weapon that has three attacks in which an unheirloomed Short Falchion/Nordic Sword outdamage it and one very powerful attack that is of situational use at best thanks to the Espada not having the accompanying reach to really take advantage of it.
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This is what I've written so far; I am currently working on 2h and will move on to poles after that is finished. Now obviously, everyone is going to have a different opinion on this kind of thing, but are there any glaring omissions of or errors about certain items? Is the formatting, tone, and style acceptable? Is it informative but to the point? Any criticism is welcome.
Also, does the Elite Scimitar deserve a mention in the 1h section? I know it's quite a common MW, but I'm honestly not sure why. The NCS is better unless you are someone who specifically wants a sword that does not have a thrust, in which case there are options besides the Elite Scimitar that are arguably better.