It's now 2017 so this is much easier than in 2012.
Start with either:
Both are free to start, well documented, capable in the long term. As you get started in what you need, then look to see if perhaps a different single solution or combination of solutions makes sense for your budget, number of devices, and skillset(s).
For those interested in how it was in 2012 and the next several dozen months, it was a bit harder to manage iOS since the tools and iOS itself didn't have the hooks and maturity for this function. Then, the least expensive way to manage iOS mobile devices is to use the iPhone configuration utility. It is free, runs on Macs and Windows PC and you can email and host the configuration profiles on traditional web and file sharing solutions. I'm amazed it's still called the "iPhone" utility since it long ago became the iOS configuration profile utility.
The free support method would be FaceTime and iMessages and you can have your users take advantage of Apple's free tutorials, guides and retail worships and training. Past that, some businesses prefer to enroll in Joint Venture for training where your core team can get personalized business level training from Apple.
The next level of mobile device management would be Lion Server or one of the pay as you go MDM solutions like Robot Cloud where you can get started with MDM for $5 a month before deciding if your workplace needs the extra features of a full management suite like JAMF Software's Caspar Suite or Mobile Iron type solutions.
Whether you use profiles made by the Configuration Utility or a server based solution that hooks into Apple's Push Notification Service (APNS) so you can push remote wipe and remote updates to the devices in the field - all of these MDM solutions use the built in iOS management hooks and have various costs and expenses to acquire, learn and automate controlling change to 10 or 10,000 iOS devices.
Start small, and consider that your users will be highly motivated to learn on their own. You will want to make sure you have open feedback channels and learn from them. iOS deployments generally are less IT headache than many expect and much of the learning and support can be self-paced, on-demand and as needed. Getting iPads into the hands of the decision makers and support people months ahead of a wide scale deployment is critical to remaining nimble and avoiding making decisions before you know how the devices work in your work environment. Small pilot programs are also ideal to measure and adjust deployment when you are unsure how you will ultimately be managing these devices. Hang on, iOS deployment is a fun ride.
The Xscope mirror, a free tool works without needing VNC but you need a paid companion app on the Mac to send the data.
I prefer to use screens on the iPad. VNC is the way that OS X sends it's video remotely to another display. If you don't use it, someone else needs to re-write that entire stack and it works very well for local networks.
As for why the app I recommend, it has an observe mode and seems to scale the screen much better than the Xscope app since it is designed primarily for designing, not mirroring. The same program works on iPad, iPod, iPhone of all sizes and retina or not displays. It is very fast and has an observe only mode so that you don't accidentally send touch events.
If you do decide to use it on the go for remote access, there is a free location app (similar to how Back to My Mac works) and works over ssh tunnels if you prefer more security than speed. It has great soft keyboard support and of course works with Linux and Windows as well. There is nothing I can say bad about it in terms of missing features os bugs or design.
It's a quality piece of software all around.
If you really must avoid VNC, there is another option. The Xscope app for software designers has a free companion app that runs on the iPad and will mirror your screen. It's more designed for counting pixels and looking at mockups you design on the Mac for eventual use on the iPad, but you can use it as a mirroring solution. It lacks any input from the iPad and simply sends the screen from the Mac to iOS.
It also is very high quality software - and is well designed, all around and fast.
Best Answer
Unfortunately, Apple does not allow remotely controlling an iOS device, but if you are jailbroken, you can use the Veency tweak: