The INSTALL file which comes with every LedgerSMB software release should be considered the authorative source of system requirements. In summary, the following technical components are required:
The Apache web server (others may or may not work)
Perl 5.10 or higher, with additional modules
PostgreSQL 8.3 or higher, with contribs
LaTeXor XeLaTeX from the TeTeX or TexLive TeXdistributions
Other system requirements such as required RAM and number of CPUs and their speed largely depend on the expected system activity. However, any modern VPS should provide enough memory and storage to satisfy a reasonable number of users.