Ignore most of what I just told Bill
Here is the reason why- you need to focus on how much your budget will get you. So compromises will have to be made.
Which is not a failing or as detrimental as you would think.
Regarding the Mac vs PC debate-
The Mac is a very capable machine with a good proven track record in multi-media work. However this comes at a premium.
The costs have gotten much better as of late and narrowed compared to the PC equivalent- but in general still more expensive.
Either Mac or PC can do the work you throw at them. It depends on which platform you decide to go with.
Since you are already familiar with the PC then I would stick with that for now and move on from there. Remember there is going to be added costs when you switch to another platform as well as a bit of a learning curve. You will have to buy all new software. So stick with what you know for now until budget allows you otherwise. Don't get caught up in the hype as to which platform is better- it's all marketing and personal bias coming into play. Especially if you talk to a salesman whose job it is to sell you a product.
A dedicated graphics card does indeed help. Have you tried also searching sites like Newegg, Amazon, NCIX ? Even Bestbuy for their budget lines.
The model you listed has UMA graphics which is not bad- it is an upgraded Intel chip. As I said, modern laptops are much better than past offerings and I would not worry too much about it. Just get what you can and start using it. (Also they are not that thick or heavy- most are less than 1 1/2" in height so very portable.)
Also be aware if you purchase a new budget laptop in the next few months you can sign up to Microsoft and get Windows 8 for a discount $14.99 when that comes out. It will speed up the PC- and if you don't like the new Metro start page interface you can download a couple free utils that can bypass it and give you back the desktop that you are used to. (Stardock Start8 and Classicshell from Sourcedforge.) So verify you can register for the MS discount for the new Win8 OS if you get a refurbished laptop. I don't see an issue- but just make sure.
Let me know if I can confuse you anymore- I mean help you with the confusion anymore.