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My LO also loves to drink from our regular cup, we let her do it once in a while when i'm too lazy to break out her sippy or just to entertain her if she's fussy. But personally I wouldn't want to skip the sippy because it would be too much work for me to have to constantly hold the cup or have to clean up the milk if she was using the regular cup, shes' always throwing her sippy around.

We skipped the sippy and went to the straw cup. So much easier. And all you need while out is a straw and a carton of milk from the gas station!

Also there's a trick to get them to learn how to drink from a straw... Dip the end of the straw in water and put your finger over the top, trapping a bit of water in the straw, then hold over baby's mouth and dribble the water into their mouth. Do again until they start sucking at it, then put the straw in the cup and let them suck!

My 2 1/2 year old nephew causes just as many messes with a sippy cup as he would with a regular glass. The sippy cup is treated as something that can be thrown around, so of course, he does! Yay milk in the carpet. Skipping the sippy is actually a very appealing idea...

My LO didn't take well to sippy or straw cups at first but drank fine from a normal cup with assistance. Eventually he learned how to drink from a straw cup, and it is so much easier for me. It gives him the independence, and I don't have to constantly worry about water/milk spilling everywhere.

You may need to wait and see what works for your LO. I was hoping to skip sippy cups and go straight to straw, but when LO was 6 months she couldn't figure out the straw cups. So we bought sippys and she liked chewing on them but almost never got any water out. Last week (at 8 months) we tried the straw cup again when we figured out that she could get water out of my camelbak water bottle with, and now she loves that. We have only been doing water in the straw cup but I am so glad it works.

We have been experimenting with regular cups too--lots of fun. Since my LO is in daycare I think a covered cup makes life a lot easier for her there too...

We went straight to regular cups! LO got the hang really quickly, and soon enough he could hold them on his own without spilling all over himself. It seems like you're heading in the same direction so I would go for it.
FWIW we also tried different methods for the straw cup but he didn't get it until almost 12 months. Now we use both, a regular cup at meals, and a straw cup when we go out because it's easier with the diaper bag.

I'm an early intervention(birth-3) occupational therapist, in the past I've helped kids learn to use the straw with this trainer cup:
http://www.playtexbaby.com/mobile/CupsMealtime/Lil-Gripper/LilGripperTrainingCup
It's kind of like a juice box that you can squeeze the cup for your baby to bring liquid into the straw initially, and then gradually let them practice without you squeezing. Then you just twist the lid a certain way so LO can't squeeze the cup and make a mess! I plan to try this with my little one when the time comes!
From an ot standpoint sippy cups aren't a necessary step as far as skill just a convenience! Open cup is a good idea! Straw cup can work for convenience but also carryover into when your baby is older!