Question: I'm working with a start-up, mostly doing system administration and I've come across a some security issues that I'm not really comfortable with. I want to judge whether my expectations are accurate, so I'm looking for some insight into what others have done in this situation, and what risks/problems came up. In particular, how critical are measures like placing admin tools behind a vpn, regular security updates (OS and tools), etc. 

Keep in mind that as this is a start-up, the main goal is to get as many features as possible out the door quickly, so I'll need as much justification as I can get to get the resources for security (i.e. downtime for upgrades, dev time for application security fixes).

Background Info:

* Application is LAMP as well as a custom java client-server.
* Over the next 3 months, I project about 10k anonymous visitors to the site and up to 1000 authenticated users.
* Younger audience (16-25) which is guaranteed to have an above average number of black-hats included.

Thanks in advance for your responses, and I'll welcome any related advice.

Answer: 
If security isn't thought of and built into the application and its infrastructure from day one it will be much more difficult to retrofit it in later. Now is the time to build the processes for regular OS/tool patching, upgrades, etc.

* What kind of data will users be creating/storing on the site?
* What effect will a breach have on your users?
* What effect will a breach have on your company?
* Will you be able to regain the users' trust after a breach?

Since your company is dependent on keeping existing users and attracting new ones, you should present your concerns along the lines of how the users would react to a breach. The higher-ups will understand that the users are your bread and butter.
These will probably be obvious:

* Limit password attempts.
* Sanitize your database inputs
* Measures to prevent XSS attacks

It's also worth mentioning that, as you said, the network architecture should be set up appropriately. You should definitely have a decent firewall that's locked down as much as possible. Some people recommend putting your systems between dual firewalls of different makes so that in the event one of them has a critical vulnerability, the second will most likely not have the same vulnerability and you'll be safe. It all depends on what you can afford since it's a startup.