Personally, I set ALL shields to high ...
Don't see how setting to high would affect internet or system speed.
Generally speaking, setting heuristic testing to high in any AV
can increase the possibility of getting false positives. Also,
the testing of an object - such as a Java script - will usually
take longer thus possibly slowing throughput.
In another top-rated AV product, if I set the heuristics to
Medium in the File AV component some .js files will cause the
CPU usage of that scanner to hit 99% for a considerable length
of time. Setting it to High can cause 99% cpu usage for many
seconds or a few minutes. This causes the browser to freeze for
an extended period of time when it encounters certain scripts
on some web pages until the heuristic testing is complete. With
the file AV heuristics set to Low in that AV product this delay
is avoided. So the level of heuristic testing can indeed impact
throughput speeds - at least in some AV products.