So far I have only looked into the Nexus 7 and the KindleFire HD. Does anyone have any suggestions?
The one weakness of Android is that it is incredibly fragmented. The vast majority of devices available don't actually run vanilla Android, but some heavily customized derivative of it. To make these customizations, companies invest tons and tons of money and time.
In addition to this, with embedded devices like phones, tablets, and now some modern PC's, sacrifices made for power efficiency have caused the actual hardware platforms to be non-generic (i.e. the OS is not able to query attached sensors and devices - it must be told ahead of time what they are and how they are connected). In most cases, this means the kernel source code needs to be modified and then recompiled for each individual device.
When you take the above facts into consideration, it means that for a company to design and release and Android device takes money and time in the areas of both hardware and software design. After a product is releases, a significant amount of time and money must continue to be invested into maintaining software updates for every previously released device, as updating the OS requires unique and specific modifications for each individual device.
This has lead to the official support cycle for modern Android devices to be incredibly short, usually not any longer than about two years. This is unfortunate, as you as a user may want to continue using your device beyond that point, and there may be no reason (spec wise) that your device couldn't handle the new updates. There is also no way for you to easily update the device yourself, as it isn't like Windows or Linux where you can just slot in the install disk for the latest OS and have it do its thing. You are 100% reliant on other extremely skilled individuals to hack, release, and maintain updates for you.
This is the case for all Android devices, except for Google Nexus products. Google Nexus phones and tablets all have unlocked boot loaders, meaning that you as a user are able to update your OS without too much difficulty (unlike other products that require a lot of hacking to be able to even boot from "non-official" code), and all run vanilla Android (AOSP, which means no bloatware and no weird or buggy customizations). Google also releases the source code for the OS on those devices, as well as all the necessary device driver binaries, meaning that people don't have to "hack" things to update or make modifications - they can just download the source, make their modifications in the same environment as the original device programmers, and then compile and distribute the code.
This translates to Google Nexus devices having much longer official support periods, being much less prone to bugs or accidental bricks, and performing much more efficiently than similar devices from other manufacturers.
Because of all the facts above, I would almost exclusively recommend a Google Nexus device for anyone looking for the optimal Android experience. In your case, the Nexus 7 or Nexus 10 seem like a good bet. The former is a 7-inch tablet and is extremely portable, and has now gone through two hardware revisions (Gen I and Gen II). Gen I 32GB models can now be had for $120-$150 if you keep and eye out for a sale, whereas Gen II 32GB run about $230. I'm not sure of the performance difference between to two (I leave that up to you to research), but somehow I doubt it is something the average user would notice in many situations short of playing really intense games, which are few and far between (someone correct me if I am wrong).
The Nexus 10 is a 10-inch tablet (surprise) and has only seen one hardware revision thus far. This is what I would call Google's flagship device. You can pick up a 32GB model new for about $300 (your spending limit) on a good day, and a refurbished for around $285.
Hope that helps you in your search.