Hello James, i have a simple i7 that gets old and 32 Gb of ram, no ssd, besides I am behind my personal connection and two sites turn on it. A bigger under dolphin, and the new under UNA. Currently 40 users online on the UNA site and many more on the Dolphin site simultaneously do not pose a problem, so when you say 10 users and 15 seconds to post, I thought server problem. It seems no, at least from a material point of view. Have you looked at MySQL? See maybe this tutorial, it concerns two php modules and the configuration of MySQL.
Currently I have this:

key_buffer_size         = 16M
max_allowed_packet      = 16M
thread_stack            = 192K
thread_cache_size       = 16
max_connections        = 200
table_open_cache        = 100000
max_heap_table_size     = 128M
tmp_table_size          = 1024M
innodb_buffer_pool_size = 10GB
query_cache_type        = 1
query_cache_limit       = 2M
query_cache_size        = 32

Note that I am still under php 5.6...