You say it needs to have lots of memory to store pictures and videos. You are confusing terms and ideas which could cause you problems down the road. Typically, when one speaks of "memory" in the computer world, one is talking about the RAM of a system. The RAM is volatile memory which means when it loses power, everything inside it is lost. The memory you are concerned with is not this type of memory, but rather long term storage - this is your hard drive, Where you can store files for years.
Lots of laptops will fit into your "affordable" range. Take a look at these rankings:
http://blog.laptopmag.com/best-worst-notebook-brands-2013/3
Lenovo, Asus, HP, and Samsung are the top 4 laptop brands. I wouldn't consider any other brands.
Dell makes Alienware and they are not worth the money charged.
Acer makes Gateway. You'd have to pay me to use one of their machines.
Sony hardware has generally been good, but they are notorious for putting huge amounts of crapware/bloatware on machines and gathering information on their consumers without their knowledge or permission.
Toshiba has bottomed the rankings. Personally, I have used them and never had a problem, but that does not appear to be the case any more.