Configuring PostgreSQL to match server configuration

Question

We are currently running web application and database server on singe dedicated machine. This is hardware configuration - http://www.hetzner.de/en/hosting/produkte_rootserver/ex10. Around 50Gb of ram is free. PostgresSQL takes only 600Mb while webserver processes take 7Gb. Average CPU load is 25%.

Software is Ubuntu 12.04 and Postgres 9.1. Database size is 15Gb.

As load increased our application response time increased from 230ms to 450ms over last few months. Application takes 40% share while DB takes 60% of response time.

We cached a lot of things, but was wondering if we could get something by tweaking Postgres configuration. After bit of researched we found that default PostgreSQL configuration (https://gist.github.com/darkofabijan/9453c793ceec1ac6274d) is really conservative and that we should definitely tweak our configuration.

After running pgtune we got following recommended values.

maintenance_work_mem = 1GB 
checkpoint_completion_target = 0.7 
effective_cache_size = 44GB 
work_mem = 288MB 
wal_buffers = 4MB 
checkpoint_segments = 8 
shared_buffers = 15GB 
max_connections = 200 

Once we started running our PostgreSQL server with recommended values we got somehow regular spikes when application response time jumped to 2000ms+ while increase was in database response time. After running it for couple of hours we reverted to original Ubuntu 12.04/PostgreSQL 9.1 configuration.

Obviously we don't have much experience with running DBs. Both concrete recommendations regarding pgtune suggested values and pointers to good resources would be much appreciated.

Edit 1:

            name            |         current_setting          |        source
----------------------------+----------------------------------+----------------------
 application_name           | psql                             | client
 client_encoding            | UTF8                             | client
 DateStyle                  | ISO, MDY                         | configuration file
 default_text_search_config | pg_catalog.english               | configuration file
 external_pid_file          | /var/run/postgresql/9.1-main.pid | configuration file
 lc_messages                | en_US.UTF-8                      | configuration file
 lc_monetary                | en_US.UTF-8                      | configuration file
 lc_numeric                 | en_US.UTF-8                      | configuration file
 lc_time                    | en_US.UTF-8                      | configuration file
 log_line_prefix            | %t                               | configuration file
 log_timezone               | localtime                        | environment variable
 max_connections            | 100                              | configuration file
 max_stack_depth            | 2MB                              | environment variable
 port                       | 5432                             | configuration file
 shared_buffers             | 24MB                             | configuration file
 ssl                        | on                               | configuration file
 TimeZone                   | localtime                        | environment variable
 unix_socket_directory      | /var/run/postgresql              | configuration file