Marie Stone,
I'm glad to see an author with an interest in historically authentic arms and combat.
Probably the most important primary sources for you would be the works of Fiore Delli Liberi, Philippo di Vadi Pisano, or maybe even Antonio Manciolino. Manciolino's works weren't published until the 1520's-1530's, though.
Copies of those swordsmen's works and others like them can be found at:
http://wiktenauer.com/wiki/Category:Masters
Those works teach a very extensive series of techniques with all of the weapons considered appropriate for a knight or men at arms in Italy at the time. Fiore Delli Liberi's works are the easiest to understand especially since they have pictures, but his are also the earliest.
As far as what arms and armor they would be using, that would depend on their social class and on the type of combat they are dealing with.
Only the rich could afford a full suit of plate armor - the Milanese plate armor being among the most popular designs. The middle classes would have used partial suits of armor, such as a helmet, breastplate, and gauntlets. They would also typically have a thick gambeson underneath that and possibly some maille. Even then, that would have been quite expensive.
Depending on the era and the personal preferences of the knight, a full suit of plate armor might range between 40 and 80 lbs. 70-80 lb. suits of armor were very rare though. A more realistic weight might be 50-60 lbs for the 1400s.
Regarding arms, it would depend on the situation. Longswords are a safe bet for anyone in the upper classes as they were suitable for combat in virtually every situation. That's one of the reasons ARMA tends to emphasize the longsword. Longswords (Italian Spada Longa) were also called War Swords and Hand-and-a-Half swords. Messers, Dussacks, and other curved blades tended to be more effective against lightly armored opponents since it was virtually impossible to kill a man in full plate using a cutting stroke. Killing a man in full plate was normally done via a stab/thrust to a weak point in the armor such as the eyes/face, the armpit, the groin, or the bend of the knee. Pollaxes were also a popular weapon for combat on foot against full plate clad enemies. They were big, powerful, and could be used to either dent and crush armor in on the enemy or to stab at weak points. They were in appearance a mixture of a hammer, an axe, and a spear and are close cousins to the halberd. Pollaxes also typically had a spike on the bottom tip of the shaft as well. Daggers and spears would have been used by all classes.
During that time period, most fighting men with any real money would have carried around a longsword and a dagger for self-defense. Alternatives for the longsword would include the falchion, messer, dussack, or side sword. In Italy, the side-sword was by far more popular.
The side-sword was a one-handed, double-edged, straight sword with finger ring guards allowing the wielder to put his/her index finger safely above the cross guard. It could effectively be used to cut down lightly armored opponents with the edge or pierce armored enemies with the point. It was better suited for thrusting with the point, though. The side sword was often used alone, though it could be used with a buckler, dagger, target shield, or cloak. The side sword gained in popularity during the 1500s and 1600s, so it might be better to stick with the longsword for your book. The longswords ranged from 2.5 - 4 lbs with most being approx. 3 lbs. Their blade lengths were usually 3 feet or slightly more.
The staff was also a very popular weapon throughout Europe, though it was not particularly well suited to a battlefield with armor unless it was proparly treated and had steel points. Later German schools of fencing featured such staffs (almost double-ended spears).
The weapons I would look into the most would be the longsword, the dagger, and the spear. They were considered the three main knightly weapons of the age, with the pollaxe sometimes considered the 4th knightly weapon (though the pollaxe was not well suited for mounted fighting). Regarding ranged weapons, the Italians were known for having highly skilled crossbowmen.
Another important point is to remember that fighting with a longsword without armor and fighting with a longsword in full plate armor is very different. Fighting in full plate against an enemy in full plate while both of you are on foot means that you will be "half-swording." That is a fighting style unique to late-medieval Europe in which you actually place one or both hands on the blade of the longsword and wield the longsword as if it were a short spear. This allows you to gain far greater point control for stabbing at narrow gaps in the armor. It also gives you more power in your stabbing. Half-swording techniques include far more than just stabbing at weak-points. It also includes hooking techniques using the cross-guard, smashing techniques using the pommel, lots of grappling, etc. Fiore Delli Liberi has a great section on half-swording.
If you have more questions, feel free to ask me or anyone else on the ARMA forums.
I would advise directing your questions towards ARMA study group leaders as they would have the most knowledge and experience. All I have studied so far has been from the German masters, so I could not provide much help with the actual use of the blades if you want Italian styles.
Another option is to ask Steven Reich. He specializes in Italian swordplay from the 1500s, so he would be an excellent resource.