This for 285ls (with 24 month warranty)
CASE MidiTower ATX 500W Black
CPU S1155 INTEL Core i3-2120 3300Mhz/3MB/65W BOX
MB S1155 Giga-Byte iH61 Express (mATX, 2xDDR3, 2xPCI)
RAM 4096 MB PC10600 DDR3-1333
HDD 1TB SATA 6GB/S WD
VGA nVidia Geforce GT440 1024MB/128Bit DDR3 D-Sub/DVI/HDMI
Options Integrated 1Gb LAN & 6Ch HD Audio
I/O Ports 2xPS/2, 6xUSB, 1xLAN, 1xD-SubAsap.lv
And this for 390ls, with same warranty
CASE MiddleTower ATX Black & 650W Power Supply with 120mm FAN
CPU INTEL Core i5-2400 3100Mhz/L2 6Mb Cache/ 95W Box
MB S1155 Intel H61 Express mATX (4xDDR3, 1GB LAN, HD Audio)
RAM 4096MB DDR3-1333 PC10600 (Up to 8GB DDR3 +17Ls)
HDD 1TB WD SATA 6GB/S/32MB 7200rpm
VGA nVidia Geforce GTS 450 DDR3 1024Mb/128Bit 2xDVI/Mini-HDMI
I/O Ports 2xPS/2, 6xUSB, 1xD-Sub, 1xDVI, 1xHDMI, 1xLANAsap.lv
If you live in Riga, it shouldn't be a problem getting to them. They are very kind to the customers - if you want to change the RAM to a bigger one, they'll do it very quickly and probably they will let you have a different graphics card if you ask them. Not so sure, as they may not have any in stock.
They have more PCs in your budget range (290-305ls), but they all had integrated graphics cards, so I didn't list them.
P.S. Their warranty is valid only if you don't open the computer's case.