Low-cost Android tablets frequently omit the Google apps (Market, Maps, GMail etc.) because those cost money to license from Google. If cost is not an objective then you can go for the latest Motorola Xoom (or some other higher-end tablet), and you'll have all the Google apps including Market.
Some Android devices do not allow you to install your own apps, but those I'm aware of are all phones that are obtained through a carrier, and even within that group they're a tiny minority.
I don't understand what you're asking with "do I need a higher version of Android" - for doing what? If you're serious about Android tablets you'll want at least Android 3. Again, for cost reasons, the lower-end tablets like the ones I linked to use Android 2. But Archos has higher-end tablets running Android 3 as well:
http://techcrunch.com/2011/09/15/archos-q9-tablet-is-a-beefy-honeycomb-running-machine/