Your requirements are very reasonable. But what is your price range and budget? Also if you have a higher budget you might want to consider a semidedicated or virtual dedicated solution to have higher reliability.
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What kind of projects do you want to host? If you have high traffic websites and a good budget it is probably a good idea to get your own VPS. This will allow you to customize hosting environment. Otherwise I would suggest you only one thing. No to go with overselling web host. This will be the opposite of "stable" and "reliable".
There are heaps of Hosts on the internet today, Some offering Cheap and Affordable Services and others offering slightly dearer but for a better experience.
To me, Sites offering Cheap Services are good but they may lack something. Speed, Service, Customer Service and list could go on. But I am not accusing hosts that sell cheap are really like this but a large majority are.
If it was me searching for a host of course i would be going cheap only cause it would suit me. But it pays too look around and remember you get what you pay for!!!!
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