I can't tell you what weapon I would build (because I'd rather have a weapon built for me by someone with more experience with weapon design than me), but the weapon I'd prefer to wield would have the following characteristics:
A high caliber shotgun.
Depending on ammunition, it would enable high stopping power against soft tissue in close to medium range (think buck shot or flechettes cartridge) with little penetration for maximum energy delivery, or solid shot (slug or sabot) with high impact, high penetration but little stopping power against soft targets.
Preferably a twin loading/fire mechanism, one for magazine fed, semi-automatic fire, one for tube-held, manual loaded pump action fire.
Possibly built as side-by-side barrel alignment, so that turning the weapon by 90° will have the active barrel centered.
The stock would have a revolving trigger mechanism so that only the barrel and magazine mechanics turn, so that I when ever I snap the weapon into the other configuration, the stock and trigger action stays in position and automatically snaps connected to the switched configuration.
Different weapon configurations to be able to switch between used ammunition on the fly without having to eject and switch magazin to accomodate changing combat scenarios; think a bunch of Beowolves (soft targets, engaged with buck or flechette shots for maximum damage) and then suddenly a Deathstalker (hard target, where solid shot with high penetrative power would be needed and buck/flechette shot would be next to useless). The pump-action configuration would come with a direct-chamber loading mechanism just in case I'd have to use any other special ammunition besides the prepared loadout, so I can handload a round and have it ready to fire immediately without having to spend the previously loaded rounds for it to cycle into the firing chamber.
Since I'm not a believer in fighting enemies on their ground, I wouldn't add needless melee capacities to a gun when it doesn't need them, it would only add weight and encumberance, increasing wear-down during prolonged use, which is far more dangeraus imho.
I'd of course have a high powered sidearm as fallback weapon and an utalitarian knife for survival means and when I for some reason really need or only can use something else than my guns (in case of ammunition being out for example).
My .02 dollars