Glad to see you starting Logh. It would be a good idea to watch My Conquest is the Sea of the Stars ( http://myanimelist.net/anime/3014/Ginga_Eiyuu_Densetsu:_Waga_Yuku_wa_Hoshi_no_Taikai ) since it takes place right before the start of the series and was also released a few months before the start of the Main Ova Series. The movie Overture to a New War ( http://myanimelist.net/anime/3016/Ginga_Eiyuu_Densetsu:_Arata_Naru_Tatakai_no_Overture ) is an expanded retelling with more details and character devolpment of the first 2 episodes, and is very worthwhile as well. Note it's not cataclysmic if you skip these 2 movies, but trust me they are worth it and best viewed early in the series.
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I saw your post in Ano Natsu episode 12 asking "If anyone has any recommendations on similar anime please, for the love of God, tell me!" so if you are still interested you have to check out Onegai Sensei ( http://myanimelist.net/anime/195/Onegai%E2%98%86Teacher ) and its Ova, which is nearly an exact clone of Ano Natsu and heavily ties in to it, as well as the IMO vastly superior sequel/spinoff Onegai Twins ( http://myanimelist.net/anime/196/Onegai%E2%98%86Twins ) . Anohana ( http://myanimelist.net/anime/9989/Ano_Hi_Mita_Hana_no_Namae_wo_Bokutachi_wa_Mada_Shiranai. ) is also by the same Director but is considered radically superior to Ano Natsu. Another somewhat similar series is Toradora ( http://myanimelist.net/anime/4224/Toradora! ) which is by the same studio.