How much are you looking to spend? And do you play games while not at home? It is a tough decision choosing a tower or a laptop, but I found the best way to go is build a good desktop, and get a regular laptop. Most laptops under $400.00 will run most Indie games and be able to keep you busy on the road. Not to mention 8 and 16-bit emulators. Laptops are a pain in the ass to upgrade, and components are almost double the price.
I built my first PC about 2 years ago. And was surprised how simple it was. The hardest part was choosing the components that worked together. New egg has plenty of do it yourself full systems that you can save money on and build yourself. My first attempt at building a desktop took about 6 hours. 3 of which were me trying to get the processor on. Which is incredibly easy and take literally 30 seconds. But I was scared I was going to break it. Anyway everything is color coded and super simple. You would have to be illiterate and color blind to mess it up. Even setting up windows 7 OEM is a breeze.
I would say go desktop. You will love it and can always get a cheap laptop, or keep yours. Most good builds that run nearly everything on max specs will be around $900.00. You could probably do this for much cheaper.
Here is a sample I would recommend. I highly suggest sticking with Nvidia video cards, and Intel processors if you want max compatibility. The great thing about a PC is they are very easy to upgrade.
A decent build.
Tools : flathead screwdriver and a antistatic wristband. That's it.
Components.
Coolermaster enclosure. ATX MID TOWER form factor
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119233 $59.99
at least a 500 GB hard drive Get a name brand. Seagate and Western Digital. I like the seagate barracuda's. Solid state drives are good. But a little expensive still. Stick with a regular one.
http://www.newegg.com/Product/Product.aspx?Item=N82E16822148840 $54.99
A decent motherboard. ASUS and Gigabyte are both good. Just make sure the socket type matches your processor you want to get. this is a LG1155 which works with modrn intel chips and leaves room for upgrade. It's also worth noting you need to know the chiset of the motherboard. This is the northbridge and southbridge chips on the motherboard that send info between components. Just read up on the chipset and see if it's good. If the board is rated good in newegg it's probably good.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131837 $129.99
Windows 7 Professional OEM. This is in my opinion the best version of Windows right now for gaming. As it allows windows xp and other system compatibility mode. But keep in mind old games will not run if it is 32 bit. I have got a lot of old stuff to run out of the box with windows 7 oem, like baldurs gate and other D&D games, but sometimes it is annoying like the other day when I could not get SNES tool to install or Blood Omen Legacy of Kain. $139.99
A good PSU. I highly recommend a modualr PSU. It will allow you to remove wires you do not need to keep things clean in the case and air moving. 550 watts should do the trick. But research first before hand so you don't blow your motherboard. It is better to go big. Cause if you ant to upgrade components later you have the wattage to spare. Too much will never hurt.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817152028 $44.99
A Intel CPU. Don't just look at processor speed. L2 Cache is also very inportant. That's why celeron processors suck balls.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116504 $229.99
Some RAM. I recommend at least 8GB for now
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231428 $83.99 GSkill and Corsair Vengance are usually good for gaming.
A decent video card. At least 2GB. I personally like the GTX series.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130826 $179.99
A few extra fans. Your case will tell you what sizes you have extra ports for. Usualy anly about $10.00 each you might need like 3.