Muv-Luv EXTRA and UNLIMITED are essential to know and understand what's happening in those VNs. They're the set-up stories to Muv-Luv Alternative. EXTRA is a day-to-day life experience, as UNLIMITED you'll be sent to another world (a pretty fucked up world) and you'll get to understand the characters better and some of their background stories (not much to tell anyways). And I am with you, EXTRA is freaking boring and beyond freaking stupid (Sumika's route is really dump and not developed). I did enjoy EXTRA for it's entertainment and I also did enjoy Meiya's route better than Sumika.
In my own case, I read a summary of EXTRA and UNLIMITED then played Alternative. Half-way through ... I wanted to go back and play EXTRA and UNLIMITED to get a better grasp of the character's emotions, but I ... was stuck - my freedom was lost all in Alternative. So I decided to finish Alternative then hit EXTRA and UNLIMITED. Alternative will take you more than 90 hours to beat up to 130+ hours (correct me if I'm wrong, but I put up about 110+ hours). I went back to EXTRA, and decided to go with Meiya because of how involved and important she is in Alternative (all characters are, and Meiya plays a very important role to Takeru). Meiya's route was pleasant, I really liked it. Sumika's was boring and stupid. I hit UNLIMITED and I laughed a lot and didn't have trouble understanding the characters since I played Alternative. Thou' the development and the routes and arcs in UNLIMITED are essential ... they are very important in order to give you an insight of who the characters are and what will happen in Alternative. I beat Meiya's route considering the relation and importance she is to Takeru (even the guide suggests to beat her route before the rest and you can just skip everyone else and go to Alternative afterwards - I hear they are about the same, only different words but settings are the same).
If I can go back in-time, I would play Muv-Luv EXTRA and UNLIMITED before I play Alternative. You do what you want to do, but for a full experience and so you don't end up regretting it later - do what I recommend in this statement.
There are characters from Kimi ga Nozomu Eien that make appearance in Alternative and ... I freaking screamed so hard just seeing them. No, not just Akane.
I'll put Alternative in words for you to understand - it is way and above good to describe or to put into words. Alternative will suck you in and dry you - it's bittersweet, brutal, driven emotion, gory (explicit and mind-fuck scenes) - yet it's honorable, structured backstory (well put together, detailed in every corner you want to think about and explains everything - even why ... I won't even go there!), developed beyond your imagination, awe moments, respectful and ... just everything you want to have - everything in a VN is put together in Alternative. Alternative is worth it.