That is a pretty decently priced laptop peep. There are light-years worth of difference between a a4 and a10. Also, if you end up going between a i3 and a a4 personally I would go with the i3.
Why: Better cpu performance, you won't be doing any heavy gaming on a a4 processor which comes with a 6400 series GPU and anytime I see a second number after the first number as a 4 or a 5 you typically get the feeling its a home theater type card.
Although: if your intent is to game the laptop peep presented to you is a good option lenavo is a decent brand however they primarily make business computers.
Batter performance: you will probably get amazing battery life with any of the suggestions on this page because fusion solutions don't use much power neither does a i3 they aren't heavy powered gaming machines that will get you 1 hour battery life charges.
Contrary to what Intel has convinced people's mind in the past about integrated graphics being "good for only home theatre", the AMD APU's are getting down to business when it comes to medium-high gaming. Power consumption isn't that much of a deal on your overall electricity bill in the case of this laptop configuration and given that you want a budget laptop means you're a normal pc application user of office apps, youtube, facebook, twitter, bf3 etc.
The A4 setup should be surprisingly pleasant once you get into it.