As I deal with tablets regularly and have a device lab I get asked for advice on which tablet to buy. This is my advice for buying a tablet as at January 2013.
There are three key decision points when choosing a tablet: operating system, size and mobile data capability. I'll run through these in reverse order.
Mobile data capability
Most tablets these days are available in a version with mobile data capability - that is to say they will take a SIM card and can connect to mobile data networks. This is undeniably convenient and gives the kind of always-on connection that you have with a smart phone. However if you have a smart phone then you already have a device that has an always-on connection so it might not be such a priority to have this in your secondary device. My recommendation would be that, unless you know you want mobile data capability, you get a MiFi portable WiFi hotspot. The data plan for this should be the same as that for a tablet data connection and it can be used for any device that has WiFi - such as your tablet, laptop or even phone. I have had one of these for some time now and it's incredibly useful, not only when there is no WiFi but also when "free" WiFi is offered I find it much easier to use my MiFi - it's also a godsend if you are behind a heavily restricted corporate internet gateway.
Currently (January 2013) the two main sizes for tablets are seven inch and ten inch (or some reasonably close approximation). There's a lot to be said for both and, ultimately, you're going to have to choose for yourself.
The obvious advantages of seven inch tablets are that they are cheaper, and smaller, lighter and more portable. Whilst not quite pocket sized, if your main concern is portability then a seven inch tablet is going to be better for you. At about the same size as a paperback page, the screen is big enough for most content and web sites and most apps that you use on your phone will benefit from the extra space.
The main advantage of a ten inch tablet is, unsurprisingly, that the screen is much bigger. The difference isn't trivial, there really is a lot more real estate on a ten inch tablet. If you want to use your tablet as more of a laptop replacement or plan to use it for content consumption such as reading books and websites or watching videos then the extra size makes this much easier. If you are planning on reading comics then ten inch really is the only choice for you.
If you have an iPhone then get an iPad, if you have an Android phone then get an Android tablet - in either case the apps you have purchased on your phone should be available on your tablet. If your phone isn't Android or iPhone then you'll have to chose for yourself. I've done a hands on review of the Microsoft Surface RT and it's a waste of money - don't buy one. I've not used a BlackBerry Playbook so can't offer any advice regarding this.
If you are going for an iOS tablet then you have two choices - iPad or iPad mini - and, if you've already chosen your size and data connectivity, then all you have left to choose is the amount of internal storage, as there is no expansion capability for the iPad you are limited to what's on the device so get as much storage as you can afford - especially if you intend to use it as a travelling media player.
There are a number of Android tablets on the market but for seven inch I'm going to recommend the Google Nexus 7 as this is well spaced device at a reasonable price point and is a Google reference device so should receive device updates. As with the iPad, this does not have an expansion slot for extra memory so buy a device with as much storage as you can afford. If external storage capability is something you want then the seven inch Samsung Galaxy Tab 2 is probably the best bet.
When it comes to ten inch Android tablets to my mind there's one obvious choice and that's the Asus Transformer. The Transformer is a good tablet in its own right with a nice screen, microSD card slot and micro HDMI output but it is when coupled with the keyboard dock that it excels. The dock features a good chicklet keyboard, touchpad mouse controller, SD card and USB ports and a battery that will top-up charge the tablet when docked. With the dock it becomes a true laptop alternative with a keyboard that lends itself to more than just casual text entry - this entire article was written and edited on my own Transformer - and the additional battery, combined with the power saving processor mode, gives it fantastic battery life - significantly longer than most laptops.
The Kindle Fire is an interesting option for a tablet. If you are in the UK then only the seven inch versions are available but the larger nine inch version is available to customers in the US. The Fire uses a heavily customised version of Android 4 as its operating system and is geared completely towards consuming Amazon's content. If you are looking to read books, browse the web and watch films and don't mind being tied to Amazon then the the Fire could well be a good choice for you - especially if you have, or get, an Amazon Prime account as this will allow you to "borrow" books at no cost.