Prog is weird and it intents to be. You will often be challenged hearing stuff you haven't. Be that instruments, rhythm or song structure. Its just meant to be goofy and over the top. I don't want to dismiss all modern progressive rock out of hand but much of it is trying to sound like styles within the style of 70's era progressive rock. There are bands like Porcupine Tree and Opeth that do their own thing progressively but there are many that sound like copies of the older bands.
I really recommend you go back to the source for this, its the cleanest at the original. I am always going to recommend Rush, Yes, Pink Floyd and Gabriel era Genesis. But I recently heard wind and the wuthering, that isn't that bad, its not a rocker but its alright. Blood on the Rooftops is nice. I think that is worth a listen as its still in the progressive era of Genesis. But stuff like Watcher of the Skies and The lamb lies down are probably the first you should give a listen.
Yes you are not going to go wrong with I recommend the Close to the Edge record first. But Even the very early stuff is fantastic. I do like the going for the one record. You can try the Trevor Rabin stuff if you are into 80's pop. The songs are not terrible for what they are, they just are not really progressive like the longer format stuff they did in the 70's
For Pink floyd I want to get Meddle. Not Dark Side, Not the Wall, Meddle. This is a great start that is nothing like what you have heard on the radio. This is quiet and folky but prog. It doesn't have the weight of the music machine behind it either. This is a band able to do what they want and forging something new. There is a large amount of what is to come hidden there to find for the careful listener.
Just get Rush's 2112, it will give you some progressive rock cache and its a hell of a record. This is a rocker it's not hard to like. The music is great and it flies its flag high in hand. You will need to listen to what is being said here as its a strangely conservative message for a rock record. I sort of image Ron Paul has a copy of this record hidden away somewhere.
You next steps will be Saga, Gentle Giant and Camel. Avoid the Krautrock stuff for now. It's great but too much of that too early on and you may end up an evil scientist.