Hello Lehi,
the full BGP table requires approximately 128MB of DRAM, although that depends on factors such as the number of BGP peers, filters, attributes etc.
The 1U switches such as the the 3560 are not really suited for your purpose. You need a chassis-based L3 switch such as the 4500 or 6500 in order to support the full BGP routing table.
HTH,
GNT