Best primary weapon for all zombie types would be a sound suppressed firearm mounted with an optical sight, preferably a sidearm that allows you to carry a suitable amount of ammunition without too much encumbrance and is ready for hasty action when necessary.
Shrieker zombies (the freshly-dead zombies not in advanced states of decay which still maintain heightened states of sensory perception) can and will alert a throng of common Shamblers to the location of gunfire and other high decibel organic noises, so this type will have to be eliminated first without alerting other nearby Shriekers.
Eliminating Shriekers means you'll need a firearm that suppresses very well, is economically suitable for your carry load, and is accurate enough for short range headshots so as to not require unnecessary follow-up shots because of misses or indistinct hits to the zombies' non-vital animation control system. This points to a suppressed pistol firing large caliber subsonic rounds: .45 ACP and a well-mounted industry grade sound suppressor. The need for illuminated Tritium night sights and even a small red dot LED-style optic should be obvious.
While you'll certainly need heavier firepower spread out amongst your band of survivors, the sort of silenced pistol described above should be regarded as the primary Shrieker eliminator at ranges up to 50 meters, and possibly out to 100 meters. Remaining Shambler types of zombies, including those in advanced states of decay which have little to no sensory perception at all, can be eliminated with regular gunfire and hand combat weapons once the Shriekers are downed.
Hunters and Boomers/Vomiters can be bypassed or eliminated from long range using tactical rifles while you're perched in a hardened safe position from the zombie horde.
Remember, all you have to do is make it through the expected three or four weeks of the zombie pandemic before even the zombies in the least state of decay start to de-animate and become no longer a threat to living biologicals. You do not need to engage and eliminate every zombie if you know how to minimize your presence.
I’m assuming zombies can’t swim and I could easily last 3 weeks on a pontoon raft out in the middle of the lake.
I would take a guess you have played Left for Dead? Very Fun Zombie Game.