I'm looking to get an Android tablet I could use to look around the Google Play Store and also to hook up to my TV to play some movies, but I'm lost as to which one would be the best to get for the functions I need and still stays within the budget. I basically would like one that is easy to wire to the HDMI of my TV and possibly one that would run apps without lag since I also hope to play these games on a wide screen. I'm hoping to find one around $150 - $200. Any ideas?
You scared me by saying budget tablet. Never, ever spend less than $150.00 on a tablet unless it's the Amazon Fire 6". There are $90 tablets that sound good but will fall apart BEFORE you even take them out of the box. At that $150-$200 range, though, your best bet is the Samsung Galaxy Tab 3 or 4. One of the Toshiba tablets costs $200 and runs full Windows 8.1 I'd spend an extra $20 and get a Nexus 7 (2013) tablet, though. It's got the best performance of any tablet under $225.
I was going to also suggest either the Samsung or the Nexus 7, particularly the Nexus 7. Since they are now releasing the 9, the price should drop a bit more in price. Another option, if you can find it, would be the HP Slate, that's a rather decent tablet and maybe the Asus MemoPad. Look for those and then make a choice.
I don't know what your exact preference is but as far as tablets are concerned, you can try the Asus Nexus 7 (32 gig version). It's considerably affordable and it's got okay specs too. It's fast, doesn't lag as much as the other budget tablets and is powered by Google itself (you can guarantee a better Google Play experience). I like Kindle Fire too but it's mainly an e-book reader.
I would also suggest to look for a nexus 7 as they are the best in the range. I love their excellent performance and the service they offer all over the world. It has everything you need but does not support the usage of sim card as I had expected it to. Other than that it is really a best tablet in the range.