Rain, by itself, won't be a problem, most of the time. It can make seeing out difficult, and some aircraft do have real problems in the rain, but that's mostly aircraft with slick wings (laminar surfaces, found on high performance wings and some experimental aircraft). The Piaggio I used to fly definitely suffered in any visible moisture, including fair weather cumulus clouds.
Reduced visibility is one problem. Embedded weather is another. Be careful of running into weather that you can't see, especially weather that's hidden by the rain or the clouds.
Rain is descending and creates descending air; a lot of descending rain can be found along with a lot of descending air; this can lead to shears and microbursts and other related activity, which can be hazardous to you. In some cases, a high ceiling looks safe, and rain and virga don't appear to be a threat; they can be, and other things may be lurking in there too. Taller convective activity (thunderstorms) that are embedded in the clouds can look very much like the rest of the cloud base, but can have microbursts, hail, and other activity that could hurt you.
Last year a local instructor that I know, admittedly not the sharpest crayon in the box, but a guy that owns five airplanes, runs a repair station, and works as a Director of Maintenance for a large airplane repair facility, encountered weather that did major damage to his aircraft. He was in a Tripacer, flying home from work, and decided to go around a cell. On the back side of the cell he encountered a shaft of hail which did substantial damage. The aircraft was pelted and damaged, and rendered unairworthy. His windscreen was shattered and he was hit with hail in the
cockpit.
I've had light rain turn into instrument conditions very rapidly, and turn into snow, ice pellets, icing, heavy rain, and hail, unexpectedly. Weather isn't a new subject for me: I've been involved in atmospheric research and even thunderstorm research, flying aircraft in and out of thundercells and other types of weather, and I'm acutely aware of the hazards of weather. In a light airplane, however, especially one without radar, and without a good understanding of what's out there, you do stand a chance of becoming a victim in weather. Avoiding it, particularly in light single engine airplanes as a low time aviator, is a good idea.