I use a pink chlorine cleasner and an assortment of bottle nad carboy brushes to clean my equipment and then an acidified sulphite solution to sanitize it. My biggest concern with my basement setup is stuff not getting peroperly dried and developing mold in any leftover liquid , or dust or spiders getting into empty carboys that I can't reasonably store upside-down so I'll often sanitize and close (lid or airlock) my cleaned equipment if it's something like a carboy that I can't easily drain and confirm dry. I run cleanser and sanitizer through my hoses and tubing and racking canes and then hang them so they drain and dry, generally if you clean them right away you don't need to worry about stuff sticking to the insides, but if you ever do wind up with scunge in a hose, a spoonful of dry rice in with the cleanser can help scrub parts you can't otherwise reach, though it's going to require some agitation to make sure you get the right spot scrubbed. I'll leave a foot of air in the tube then put my thumbs over the ends and shake it around and lift one end to get the rice to the right spot, shake it some more, repeat till it's clean... then rinse really well and don't clog the drain with the rice.
I've never heard that dish soap can actively harm equipment but because of the suds, depending on your water it may not rinse out well (even a small degree of hardness in your water can leave soap scum deposits), and you really want your equipment as clean as you can get it.
My only caution with the pink cleanser is it can make the outside of things very slippery, not at all what you want when handling a 5 gallon glass carboy! I suspect the alkaline PBW that Squatchy linked may have similar issues, if yo've ever used baking soda or washing soda you'll understand... I try to keep it limited to the inside of the carboy I'm cleaning.
Another thing that helps with rinsing the cleanser out is a bottle washer faucet attachment, I use it when I rinse carboys and wine bottles. Mine looks like this
https://www.kegland.com.au/products/faucet-jet-carboy-and-beer-bottle-washer, most brew places carry something similar.