From what I've seen, read and experienced (with some previous JuJItsu training as well), in Aikido, I would say the core basics are:
Ukemi (mae, ushiro, yoko)
Kamae - basic stance
Tenkan - standard method of moving, helps blend with uke during techniques
Kokyu Ho - breath technique, standard exercise
Tai no Henko - Basic movements
Ikkyo - A very common technique to get uke to the mat. Can be done on its own, or in combination with many other techniques, e.g. -- nikkyo/sankyo -> ikkyo, ikkyo -> kotegaeshi, etc.
Nikkyo - Standard wrist lock for controlling uke
Sankyo - Another form of controlling uke
Shihonage - Probably my favorite (and best) technique - teaches how to tenkan, shift weight, maintain balance, sword movements (bringing the sword (elbow) up, and cutting down to throw.)
Finally, core...not techniques, but rather principles that *I'm* getting from Aikido:
• circularity
• zanshin
• sword-based movement
• moving from the hips
And finally for me, absolutely essential is an eagerness and willingness to learn
-Bryan