1) The diatonic is easier than the chromatic
I would say the diatonic is easier in the first few weeks to pick up the pace and get started playing simple songs. In fact I could teach you how to play "Mr. Tambourine Man" in 10 min during a lesson at my studio in Manhattan! So yes it's fairly easy at the very beginning. Now If your end goal is to play like Bob Dylan you’ll probably be better off with a Hohner Special 20 in C and a couple of tabs than a chromatic harmonica. Nothing wrong with that but there is so much more to play!
If you aim higher and have desired to imitate let’s say Paul Butterfield or James Cotton there will be a lot more work to do. You'll have to learn how to play clean single notes, accurate draw and blow bends, learning riffs... At the end the diatonic is hard as any instrument!
2) You have to read music
Wrong. You can play the chromatic harmonica without knowing solfege. In fact I would encourage you to play by hear if you’re just getting started. Explore the various registers, listen to the sound you’re producing even if you’re not sure what note it is and take awareness of your breathing. See it as a game. Stan Getz said once in the interview with Mel Martin "When I'm really free. I like to play totally by hear, knowing the basic structure of a song." It will develop your intuition and hearing skills.
There are also tabs for the chromatic harmonica with numbers indicating which hole to blow and draw. It works well if you have already the song in your head but it might be more challenging to figure it out if it is entirely new to you. You’ll be playing the right notes but missing out on a huge part of music notation, which is rhythm.
Even though reading tabs is a great way to begin and can bring immediate satisfaction you’ll be much better off in the long term learning basic solfege whether you want to play the diatonic or chromatic harp. It will also serve you on any other instrument you would like to learn.
3) You have to start out on a cheap harmonica
Completely wrong. No matter what instrument it is not going to play any better or worse as long as it a decent 12 hole airtight harmonica. Whether you buy a Suzuki Chromatix at $190 dollars or an Amadeus Hohner (see pic below) at $1700 you’ll still have to put the work, learning your scales, arpeggios and harmonica techniques. Now I do recommend getting a chromatic harmonica from a known brand such as Hohner, Suzuki, and Seydel. They will sound better out of the box and can be sure of the quality.
I think getting a very expensive harmonica is not going to make you play better or worse. If you want to get a high-end model go for it. Don't forget to hold it in your hands, see how it feels and check out the weight because some expensive brass comb models are quite heavy.
If you liked this article you might want to read Best Chromatic Harmonicas of 2017