your daughter isn't going to be doing anything like photoshop, statistical analysis or video rendering is she?
under $200...unless you want to go really walmart cheap low end, $200 or less is not going to be possible. what make/model of graphics card are you planning on putting in it? gonna make a bit of a difference in the power supply ratings.
Antec High Current Gamer Series HCG-520 520W ATX12V v2.3 / EPS12V v2.91 80 PLUS BRONZE Certified Active PFC Power Supply
newegg - $58.99 + free shipping
AMD Athlon II X2 250 Regor 3.0GHz 2 x 1MB L2 Cache Socket AM3 65W Dual-Core Desktop Processor ADX250OCGMBOX
newegg - $59.99 + free shipping
ASUS M4A78LT-M AM3 AMD 760G HDMI Micro ATX AMD Motherboard
newegg - $65.99 + free shipping
not a biostar fan but - Biostar A780L3L AMD 760G Motherboard - ATX, Socket AM3, AMD 760G Chipset, DDR3 1600MHz (O.C.), RAID, SATA 3.0 Gb/s, 6-Channel HD Audio, Radeon 3000, Fast Ethernet
tigerdirect - $49.99 + shipping
Western Digital AV-GP WD5000AVDS 500GB 32MB Cache SATA 3.0Gb/s 3.5" Internal AV Hard Drive -Bare Drive
newegg - $49.99 + $2.99 shipping
Western Digital 320 GB Caviar Blue SATA 6 Gb/s 7200 RPM 16 MB Cache Bulk/OEM Desktop Hard Drive - WD3200AAKX
amazon - $39.99 + free shipping with amazon prime
Corsair TW3X4G1333C9 XMS3 4GB 2 X 2 GB PC3-10666 1333Mhz Dual Channel 240-pin DDR3 Desktop Memory
amazon - $29.99 + free shipping with amazon prime
PNY Optima 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Desktop Memory Model MD4096KD3-1333
newegg - 27.99 + free shipping
SAMSUNG CD/DVD Burner 22X DVD+R 8X DVD+RW 16X DVD+R DL 22X DVD-R 6X DVD-RW 16X DVD-ROM 48X CD-R 24X CD-RW 48X CD-ROM Black SATA Model SH-222AB - OEM
newegg - 19.99 + free shipping
lowest possible total - $264.43 +/- unless you want to go down and dirty salvation army thrift store level parts.