You really don't know what you've unleashed.
I definitely think this album is central to anyone's pop education, and anyone that disagrees can take several seats:
Some people say that the Immaculate Collection is dated, I don't want to know those people. In terms of pure pop, this is flawless, and basically the genesis of female pop as we know it today. You may have to get over a hump with the 80s sound, but it's so worth it when it clicks. You'll have picked up most of these songs over time anyway, considering they're all basically part of the public consciousness. If anything ever sounds clichéd, please be aware that the cliché originates here, and so much has been derived from the songs in this album that it's ridiculous. It's technically an 80s greatest hits album, but I think it's better this way. The only album you'd really have to go back to on its own merits is Like a Prayer. For the genesis of male pop, I'd recommend
Thriller, because MJ is flawless (and that's basically a greatest hits album in itself).
Recommended Tracks: Into The Groove, Express Yourself, Vogue
Alternatively, considering you like Gaga, I'd say Confessions on a Dance Floor basically created the blueprint for modern dancepop, so that'd be a good start if you want to hear the best of recent Madonna, and an album that will be a little easier on your ears. Just make sure it's the Continuous Mix, that's very important to truly understand the album.
Recommended Tracks: Hung Up, Get Together... you really need to go through the album in order. Forbidden Love and Isaac are personal favourites tho.
My personal favourite Madonna album is Ray of Light. However, I don't think it'd be the best jumping-off point for you and I think it's easier for you to get into Madonna from one of the above two albums considering where you're at, but do try it if you're in the mood for something that's possibly a little bit different (but not too different, it's still pop music lol). Ray of Light is really the genesis of electronica and Eastern influences in modern pop music (if it ain't then I don't know what is tbh), and it's even more remarkable contextually when you consider that her contemporaries had become Britney Spears, Christina Aguilera etc and this was really her first time going up against younger women and beating them at their own game. It's proof of how she (used to) raise the bar and go her own way. But really, the entire discography is worthwhile. Erotica, Like a Prayer, Music, Bedtime Stories... no two albums are ever the same, you could just listen to Madonna and you wouldn't get bored (well, you would, but that's why this post keeps going).
Recommended Tracks: Ray Of Light, Skin, Frozen