Yes, you'll need to change about everything except the case itself. You can still use HDDs and ODDs but they're so old by now so I wouldn't recommend it.
The Radeon 5770 is a good choice but I would recommend you to look at Powercolors cards instead that are a few pounds more expensive but much more quiet.
A "brand new" computer for FS X (and new games) would be around 520Â£
PSU: 380w Seasonic S12II-380 PSU, 12Cm fan, active PFC RoHS +80%
HDD: 640 GB Western Digital WD6400AAKS Caviar Blue, SATA 3Gb/s, 7200rpm, 16MB Cache, 8.9 ms
Memory: 2GB Corsair Value Select, DDR3 PC3-10600 (1333) Non-ECC Unbuffered, CAS 9-9-9-24 (2X)
CPU: Intel Core i3 530 Dual Core Clarkdale 32nm, 2.93GHz, 4MB Cache, 73W, Integrated GPU @ 733MHz, Retail
Motherboard: Gigabyte GA-H55M-UD2H, Intel H55, 1156, PCI-E 2.0 (x16), DDR3 1600/1800/2133, SATA 3Gb/s, VGA, uATX
Video card: 1GB Power Color HD 5770, PCI-E 2.1(x16), 4800MHz GDDR5, GPU 850MHz, 800 Cores, DL DVI-I/ HDMI/ D-Sub
Case: Asus TA-9L1, Black Midi Tower, Case w/o psu
ODD: Samsung SH-S223C/BEWE 22x DVDÂ±R, 12x DVDÂ±R, DVD+RW x8/-RW x6, SATA,BEIGE with black Bezel
Total 514.37 excl shipping over @ scan.co.uk
You need at least 100Â£ more if you want a branded / prebuilt computer with similar specs.
When it comes to laptops all you can do (that will affect overall performance) is expanding memory and installing a new HDD.