What should I look at for managed hosting?

If you're doing managed hosting, you should look at the level of management they give you. In essence, the level of management is negatively correlated to the level of freedom you have. For those who don't know how to take care of a server, that's a good thing. For those who know what they're doing, it can occasionally be frustrating. The key is to investigate which aspects you want managed versus the parts you want to do yourself and choose the best service provider for your needs.
For example, you want to look into their backup, redundancy, and security features. If you don't know how to do it yourself, you definitely need them to take care of backups and security. Backups are necessary for worst-case scenarios, and security is a field unto its own that you want to leave to a professional. It's a full-time job.
As far as the guts of the server you're working on, you want to make sure that you have enough RAM, processing power, and bandwidth to fit your needs. As a rule of thumb, it's always better to have more RAM than you think you'll need because your website will always be expanding its requirements. To give you growing room and ensure you have no problems, multiply the amount of disk space you're using times 1.5 and use that as a guideline for the amount of RAM you should get. It's worse to run out than to spend a few extra dollars on RAM.
Also, check whether or not it's “burstable” RAM or a solid (guaranteed) RAM value. Burstable RAM means that you will have a lower amount at peak operating hours (when the servers are busy), but you will have more when it's not busy. A solid RAM amount will mean that you always have the same amount of RAM dedicated to your VPS at all times. Some Content Management Systems and web-apps can eat up a lot of your RAM, so you should first try to choose the most efficient applications and then try to choose the best deal on the amount of RAM you need.
More aspects you need to consider include: application availability, control panels, and technical support. You always want to be able to install new applications whether or not they install it for you. Sometimes, new applications come out which are much better than what you have, and you want to be on the cutting edge. A high-quality control panel is also essential as it allows you to perform all of the actions necessary without having to call the technical support and request it to be done. Tying all of that together is the technical support system — if the tech support for your hosting provider is bad, you'll lose days waiting on them when you could be making money with your website.

How much will all of this cost?

Finally, you should look at the cost of the services you're buying. It's more important to choose good services and pay more money, but the cost of services is a factor that shouldn't be discounted by any means. A provider may list a low cost yet add a ton of unreasonable fees for things you would expect to be included. An example would be the cost to upgrade RAM. Normally, you would expect them to charge a monthly fee for an increase in RAM, but some companies may charge you an initial upgrade fee (which essentially buys the RAM you want), and then they will charge you a monthly fee for the increased RAM!
Keep an eye out for these types of hosting providers because that is a sign of a company which will nickel-and-dime you every chance they get.
VPS hosting can range from $10 to $100, but the primary aspect you should keep in mind is whether you're getting everything you want for the price you want.