Can you recite from the middle of a surah in salat?

I generally (or always...) recite an surah in last teen surahs in Quran. Nowadays I have free time to memorize some new surahs, and I want to recite them in salah so that I won't forget. I did some lookup, and It seems that I need to recite at least 3 ayahs after al-fatiha. Does these need to be from beginning of surahs or, for example, can I read first 3 ayah of a surah in first rak'ah and second 3 in second rak'ah? Also, does it matter if ayahs I recite make a meaningfull context? I mean, might taking random 3 ayahs from its context be wrong? For example, fourth ayah of Al-Baqarah start with (wa) "and". Would it be inappropriate for me to recite 4th ayah, without first reciting 3th ayah?