I believe it's important to minimize the chemicals in your home if your have rosacea, so I recommend natural cleaners. Don't fall for all the hype around "natural" products, though!
A lot of products sold as "natural" aren't any different from traditional products, which is a pain. You have to read labels and avoid ingredients like sulfates and phthalates (contained in fragrances), for starters.
One way to do that is to make your own. I make my own spray cleaner with just water and rubbing alcohol, about 1 part rubbing alcohol to 3 parts water. It's a great non-streaking cleaner that disinfects as well.
For a great homemade cleaner for toilets, tubs and showers, I sprinkle baking soda all over and then pour on white vinegar. It will make a minor explosion of bubbling that will bust off any grime. It's great for sinks especially as it helps keep your drains clean. I even managed to get a clogged drain reopened by repeated treatments of baking soda and vinegar and hot water. If you don't like the small of vinegar, don't worry--the smell goes away after you rinse the vinegar off. A friend of mine also sprays her couch cushions with a mixture of vinegar and water periodically to eliminate pet odors. I have used baking soda on my carpets as well.
For laundry detergent, I like Seventh Generation detergent. It cleans well and seems to leave no residue, which is the problem with many detergents. Well, actually the problem is likely your water and the detergent not fully dissolving in your water, which then leaves a residue on your clothes. Many cities publish a water test in their city website, so look yours up and see how soft your water is. The harder it is, the harder it will be for detergents to dissolve. When that's the case, you may have to add something like vinegar to your laundry to remove the residue.
I admit I miss the nice fragrances of some cleaners, but for what I have saved by making my own cleaners, I got over it. Plus, my skin is less irritated, and that's the best part!