Before considering any hardware upgrades, it is advisable to find out what hardware part is the bottleneck for the performance of your site and if it is possible to eliminate the problem by some kind of software adjustment. To do this, you would review web server logs and control panel stats for the times when you noticed the server being slow or timing out (if your panel keeps such stats like cPanel). The logs should give you the idea what parts of the site are being accessed when the problem happens.
If your server does not have cPanel, to get the idea what server resources gets maxed out, you would add a cron to run each minute and saving "date" and "top" command results. Something like
date; top -n1 >> /root/usage.log
will keep the results in /root/usage.log file.
If you need a help with reviewing the logs, advise the techs with the times when you noticed the performance issues. Also, they will be able to help with interpreting the "top" command results or your control panel stats to locate the culprit of the server issues.