One of the strengths of Mordheim is that there are so many choises to be made. When you start your band, you can't afford to buy all the heroes AND give them all the toys you want AND afford the henchmen that are so badly needed in order to win those first games.
One of the challeges of playing Mordheim is to find the combinations of weapons, armour, equipment and skills that are best suited to the way you intend to use your models in the games - and then use each model in the way you have equiped it to be used.
What I recomend here assume that only the items from the rulebook are used, as my group don't use equipment from Town Cryer, official or not! So check my resoning and check if you have access to some better items in your campaign.
Any hero that are allowed to, should have one long range missile weapon.
The coice of missile weapon depend to some degree on weather the model has access to shooting skills, as you need the skill 'Nimble' in order to become truly effective with any move-or-shoot weapon. On the other hand, a hero can get Hunting Arrows to his bow.
A bow with Hunting Arrows has about the same chances as a crossbow of taking someone OOA. The crossbow is, however, the better choise if you can live with stunning or knock down the target. If people start using armour the crossbow become an even better choise.
You could use a handgun, but then you need 2 skills in order to move and fire each turn. Not very attractive for the benefit of only +1 against armour saves.
My recomendations are:
A hero with shooting skills: Take a crossbow over any kind of bow. The S4 is more important that Hunting Arrows.
A hero without shooting skills: Take a bow (any kind) over a crossbow. Move-or-fire makes a bow with Hunting Arrows a better choise.
Henchmen: A mix of bows and crossbows can be usefull to give both move-and-fire as well as some S4 shots. Only use handguns if you are up against people with 3+ armour saves and only on up to half your shooters.
Anyone that can use a sling should get one. Slings are cheap and are far better than nothing - even if I can't get them to work for my bands.
Any hero that can use a crossbow pistol should get one as it allows one extra attack in the first round of close combat. But don't buy this toy before everyone has decent missile weapons AND some kind of close combat weapon. Crossbow pistols are 'Nice to have', not 'Need to have'.
Any hero that can use dueling pistols should get at least one of these as they are among the best weapons to use in close combat having +1 to hit as well as S4 on the first attack. But check if your group allow a model to exchange the pistol for another weapon after the first shot or at least allow the model to use the pistol as a normal mace for the rest of the melee. A normal pistol can be used instead of a duelling pistol, but then the effect is not so great.
You want weapons that improves your chances to survive in close combat.
The best way to survive is to take your opponet OOA.
Use theese guides to choose your weapons:
2 attacks are much better than one - don't even think about a shield or buckler in melee until you have 4 attacks even if you use one.
The best 'normal' weapons are: sword (parry), spear (first strike w/spear) and mace (concussion damage).
Sword & spear are the 'agreed on' defensive choise.
Sword & mace are the 'agreed on' offensive choise.
When heroes gets 3-4 attacks the chance of parrying become so small that spear & mace might be better than the 'agreed on' choises.
Some bands have some uniqe weapons. Theese weapons are normaly better than any normal weapons
Skaven has a dilemma on weeping blades and fighting claws (FC). The problem here is that Art Of Silent Death only works with fists or FC, but FC don't allow you to use slings or throwing stars.
Sisters of Sigmar has to choose whips or sigmarite warhammer. The choise depends on the whip-rules you use. Personally I have 2 heroes that have 2 sigmarite warhammers each and the rest of my entire band has 2 whips each (except hired swords). If you can whip without declaring an charge whips are the choise - even against possessed.
Rule #1: don't ever buy armour when you start a band. Armour are not costeffective in Mordheim; too many S4 or better hits are comming your way and 1/9 hit you get become a crit wound that don't allow an armour save.
When you are more or less wellequipped, you can start buying armour:
Those that are never to get involved in melee can use light armour and a shield. You save some money and get the same protection as heavy armour.
The brawlers need heavy armour or - if you can afford it - gromnill armour.
Don't ever use a shield if it will slow you down.
The no-brainers are: lucky charm to every hero, healing herbs to every hero with more than one wound, hunting arrow to those with bows.
I recomend rope & hooks if you like to climb, but then I have had my skavenboss fall 5" - and he had I6 & rope & hook!!
Lanterns will be usefull if your opponent likes to hide from you.