There are loads of problems with surviving the first few hours of a zombie outbreak.
Information on the outbreak due to the low number of infected people. The outbreak would basically go unseen to an extent. One or two people being bitten by other people is not going to ring alarm bells.
You could go in to do the weekly shop and come out to zombies everywhere. No amount of owned firearms and other weapons will be very helpful if they are at home or in the car. Also most shop owners don't like it when your packing an arsenal for a small army.
You can easily be bitten before you know whats going on or have someone with you that is bitten. No one likes driving with your mate trying to eat you.
Available weapons in an office your not going to find many M16 assault rife but a fire axe or computer monitor may be the only choice.
Those are just the short term problems long term the list is much larger.
1. food finding a good food source will become hard for three reasons zombies, sell by date, other people trying to kill you for that food.
2. Finding a save place to rest and sleep. You can't stay in one place as your get too many zombies outside so when food runs out your dead.
3. Ammo/ weapon repairs. Firing based weapons are a bit useless with out ammo. All weapons will break and become blunt fixing them is a concern or better having backups.
4. Sleep and killing as zombies make a noise that noise will wake people up a few weeks of bad sleep and everyone going to be a grumpy, slower and make bad moves. Also killing be it a zombie or a person is going to have an impact regardless of your training.
Today's soldiers are trained for combat and most come back with some sort of mental problem. The impact of killing others for someone not trained would be much worst.
5. Other people are good allies allow others to watch out and cover you. However other groups may attack you for your stuff. That nice 20 cans of cat food may feed you for a month but you may have to kill for it.
6. Existing fighting skills most combat skills and combat knowledge would mostly be useless. Blowing up an enemies fuel dump usually is helpful in a war as you deny the enemy that resource. Zombies on the other hand don't use fuel.
The combat martial arts unarmed sure zombies are slow but if they get a hold of you they aren't letting go. So perfect timing is needed all the time. Due to tiredness and being human we all start making mistakes and that leads to zombie food.
Weapons base martial arts are useful is some places. The combat training is based on cutting vital parts of the person or stabbing an organ. With a zombie on the other hand only one thing kills them that's a crushing/dismembering the head. OK cutting an arm off or a leg may slow said zombie down but it is not dieing like a person would be.
Lots of edgy weapons sold are not fighting grade but acting grade or show grade and would snap quickly. Most acting grade items would break trying to cut someones head off.
Firearms training own armies work on fire enough rounds at the enemy they die. However unless its a head shot its not going to effect a zombie.
Sometimes its better to keep it simple. A crowbar is an excellent weapon. One can crush a skull, its durable enough to not break easily and is light. Its bonus is it can open doors.
I'll add something later on.
