Caching lets Joomla store bits of information so that the site loads up faster. Unfortunately, caching things sometimes tends to be very resource-intensive, which can cause suspensions for high resource usage. I'm not all that familiar with Joomla or its plugins, but if it gives you options on caching stuff, you might be able to find a good median between having faster load times and not being suspended by tweaking the settings. In order to not trigger high resource usage suspensions, I'd start at a bare minimum (much less than the default options) and work my way up from there until I get what I conceive to be decent load times. This is of course semi-risky since as you get suspended more, you will not be able to unsuspend yourself and you'll have to post on these forums to get unsuspended.
Another alternative is to move to paid hosting where your resource limits are much higher, and thus you could run these plugins at full settings without issue.