the reason for top watering and allowing excess to drain away is to flush out the accumulation of mineral salts from fertilizer and hard water. I tend to water my Peace Lilies twice per week, but it is best to let them get slightly dry for root health as apposed to keeping them soaking wet. Don't be afraid to stick your finger in the dirt to test soil moisture. You can also use the pick it up and feel the weight method of determining how much water is in the soil. Sounds like Peace Lilies are a good plant for you as they like it wetter than most houseplants.

As for fertilizer, I use Miracle Grow potting soil, that has fertilizer in it so if you repot yearly that will probably do. Or you can use Miracle Grow liquid fertilizer in you water every other month.

Agreed. Don't water the way you currently are. Water from the top until 10-15% drains out of the bottom. Dump the water that collects in the saucer. Never let the plants sit in water.

Also, don't wait till they droop. Water when the first inch or two of soil is dry. But there's no general schedule. Water as the plants need it, not every so many days.

Anthuriums are epiphytic (meaning they grow up in the canopies of the rainforests on the sides of trees), just like orchids, and they grow in the same habitats as orchids as well. Tho they can adapt to growing in a fast draining soil mixture that's blended with orchid bark, perlite, and charcoal. They are closely related to Peace lilies. Peace lilies also prefer a fast draining soil mixture that doesn't stay soggy either. So as long as the roots can breathe and have access to plenty of oxygen, you'll never have to worry about "overwatering" them. Both of these plants live in the rainforests, where they can get rained on on an almost daily basis. So they're no strangers to water. It's a common misconception that overwatering a plant is about giving them too much water, when it's not. It's when the soil mix holds on to too much water, cutting off the supply of fresh air to your plants' roots, causing them to suffocate.

For my plants, I don't ever let them dry out. But I also use a proper soil mix that doesn't hold on to too much water either, no matter how much I water them. With it being wintertime, I don't water them as often as I do throughout the rest of the year. I have a similar sized plastic bucket that I sit my plants in and fill it up to the soil line with water, and I let them soak for about half an hour. Then I'll remove the pots and let the excess water drain away. You notice how the runoff will have a slightly brownish tinge to it from all of the dissolved solids in it. That's when I'll flush the pot out with some fresh water, until it starts to run out clear from the bottom. This helps to get rid of any excess mineral deposits and fertilizers that would otherwise buildup in the soil over time.

These plants come from the rainforest, and they absolutely love water. But they also need for their roots to breathe as well. And I don't worry about spraying them either. They'll do just fine without it.

Here's a couple of links to the Exotic Rainforest's website for properly caring for these plants. It offers a wealth of accurate information on these wonderful plants:
Caring for Spathiphyllum & Growing the Tropical Anthurium

As for the old spathes, you can just let them naturally die back completely on their own. They don't expend energy from doing this. In fact, letting them die back on their own gives them a chance to reabsorb any nutrients and/or chlorophyll from the spathes, which they can reuse in other areas of the plants. This is why they turn yellow beforehand. Once the old spathes have completely turned brown, they'll easily separate from the plant when you go to gently pull on them. This is no different than when the leaves of deciduous trees change color before the trees shed them in Autumn. Because they're reabsorbing all of the nutrients and green chlorophyll to reuse again in the Spring, rather than having to make them from scratch all over again.

Thank you all for the incredibly informative answers! It is much appreciated and I enjoy learning about these plants and how to care for them. I will definitely change my watering methods as it makes sense that watering from the top and letting them drain would be good to stop any possible build-up.

You need to understand rain water is very oxygen rich, whereas tap water is usually pretty devoid of oxygen but often very rich in chemical compounds placed in it by local authorities to kill off anything in it. So Spathiphyllums in nature often grow in water that is replenished by regular rain. I have one that has been sitting in a pond for going on 4 years now and it's doing really well. Another (variegated) one has been in another pond for under a year. The medium for both is a coarse gravel. It allows water to pass freely around the roots. They're never fertilised, they get everything they need from the water (we all know what fish do in water). When kept in a soil medium the water around the roots needs to be refreshed regularly and some air allow in. Otherwise the water stagnates and rots the roots.

Because many Anthuriums are epiphytes rain water runs over the root system and then the roots are quickly exposed to the air again. They can take a bit of drying out. As mentioned above, treated like epiphytic orchids they're quite happy.