A great start of a series, if a bit flawed.
Overall, a great game, and I am not even going to bother repeating the flaws and improvements mentioned by previous reviews, with a few exceptions that really stood out to me. Like a lot of people said, a party system would be nice, and this is something I have A LOT to say on. There are two ways you can go about making a party system for the sequels to come: the Final Fantasy approach or the Dungeons & Dragons approach. FF-style is more or less plot based, which means building your party by encountering characters. D&D-style is where you build your party from the start of the game, and go from there.
On a related subject, you should add more character classes using D&D as a guideline. Here are some examples:
The Cop: This would be your series' version of D&D's Paladin. The Cop would be extremely balanced in all combat attributes (HP, attack, defense, etc.). The Cop, however, has the charisma needed to convince an NPC survivor (please include them too) to temporarily join your party. The Cop has excellent detective skills, and can therefore locate more searchable spots on the map than most other classes.
The MMA Heavyweight: This is essentially the Barbarian from D&D. Very powerful fighter who can deal a lot of melee damage, and can wield heavier weapons such as sledgehammers with greater proficiency than The Jock. Far better success at knockbacks due to brute strength.
The Jujutsu Blackbelt: The same as D&D's Monk, the Jujutsu Blackbelt has the best melee attack accuracy of all classes. His/her melee attacks also have a far greater chance at stunning zombies (to simulate the takedown techniques of Jujutsu).
The Thug: You guessed it. The Thug would be similar to D&D's Rogue class. A typical "gangsta", his/her ranged accuracy is mediocre at best due to the way he/she holds his/her "gat". The Thug, however, is specially proficient with knives.
Now that's out of the way, weapons need a little more variety. Nunchucks, for instance, can hit multiple zeds in melee at the cost of accuracy. Ballistic knives offers a last ditch attempt at killing a zombie with headshot before it gets into melee range. Guns should be upgradable by accessories such as laser sights, ACOG scopes, red dots, etc. to improve effectiveness at either short or long range. Grenade launchers and rocket launchers certainly won't hurt either, though they should understandably be EXTREMELY RARE.
If you're going with D&D approach with creating parties, then I strongly suggest customizable characters in terms of gender and maybe stats. Also, another thing from D&D that would be good to incorporate would be the concept of alignment between "good" and "evil". This has some effects toward how NPC survivors (if you plan to include them) would react to your party. If your party is mostly "lawful good", then they are more likely to temporarily join your party or offer you items, but it will also mean they are more likely to ask you to go on quests (such as finding their missing loved ones, something you can also include), which can be a pain in the ass on its own right. On the other hand, if your party is mostly "chaotic/lawful evil", then NPC survivors would likely to react hostily to you, but can be a boost to EXP when you kill them too.
That is all I have to say at this point. I know my suggestions are rather ambitious, but please, take them for what it's worth. Besides, these are things you can implement slowly.