There's not a short answer here... Your Dad could halve his arms with your Mom's (unless they had no coat of arms). Sons bear the same arms, but with 'difference labels' overlaid. If the sons are married, they can again halve their arms (Mom and Dad's), with that of their Wife, or more usually quarter them (theirs upper left and bottom right, their Wife's upper right and bottom left).
Richard, Earl of Warwick's is a good example of how complicated things could get...
'Achievements' or puns on the family name etc, were usually shown in the choice of livery badge, which was borne on the 'standard' and not on the banner (which displayed the coat of arms only). I'm of the opinion that unless they have lands in their own right, sons would use their father's standards and livery colours.
Normally 'Lords' would not be involved in 'trade', so a gunsmith would serve a lord as a retainer. However a town or city might have a gunsmith's guild, forming part of their city's forces raised to support someone... so conceivably he might carry his coat of arms on a banner, with his guild's badge (crossed handguns?) on a standard.
These are starting points, there's loads of heraldry and related stuff on the web... but be wary that styles changed and 18th Century coats of arms were very different to 15th Century ones (they began to run out of ideas for designs as so many people were getting coats of arms). Even standards went from one or two colours in the 15th Century, to three or more in the early 16th as that became fashionable.