We picked the wrong company to put us on a WooCommerce platform and they almost put us out of business. The site is stable now, but the speed is inconsistent. We have a good hosting company and need someone that can look at the code and find what is causing the site to slow down. Everyone we have talked to is unable to find the cause.
If it's WooCommerce on WordPress, your problem is (I'm almost positive) plugins. In every WordPress site I ever worked on, the more plugins that were active, the slower it ran.
However, speed comes in a few forms: are you talking about strictly page loading speed? Or is there a certain part that drags (such as checkout)? Or something else (like the admin section)?
I'm probably more expensive than you need for something like this, but look into Copter Labs (copterlabs.com) for help. That's the agency I started and sold with 300+ WordPress builds (many using WooCommerce) under their belt, all on custom themes, so there's a deep understanding of HOW WordPress works instead of throwing plugins at it to make it do things.
Or, if you'd prefer, we can set up a short call and I can review the site and give you some insight into what's going on. Once we identify the problem, you could contract someone else to fix it.
Drop me a line if you want to move forward.
You should use a well-supported, modern theme that is built for speed.
Is the speed "inconsistent" as in sometimes a specific page is fast and sometimes it's slow? Or are the same elements always slow? Perhaps you've already done this, but run the front-end through some tests on Pingdom first: http://tools.pingdom.com/fpt/ That's where I'd start if it was one of my client sites. From there I'd run the P3 plugin to see if there was a specific plugin causing any issues (https://wordpress.org/plugins/p3-profiler/). I have a few other things I check for but these first two are easy enough for a non-tech to at least get started.