ella is almost 13mos now and our doctor suggested half formula and half milk right @ her 1yr.
I started with her naptime bottles and made them half and half but left the bedtime bottle all formula; then I slowly upped her naptime bottles to all milk and her bedtime bottle half and half. It was a gradual switch.
It has been about a month now and she is onto all milk all the time. I didn't want to change everything all at once so now we're working on not warming the bottle.
So, it's okay to warm the whole milk if you think you need to (Ella hates it at fridge temp, she will not take it) and it's okay to use bottle for milk. Ella takes a sippy fine but I still do bottles for naps and bedtime. Personally, I think it's kind of comforting through the transition to milk because the milk and formula behave differently in the gut and through digestion which can cause some discomfort.
With tap water: I don't know what doctor's suggest, but we were using tap water with her formula and we give her whatever water we drink now.
With changing to sippy cups: For Ella, she is very independent and wants to do everything the adults do, so the easy thing was giving her drinks from a regular cup(especially my cup), just like the grown-ups, and letting her help hold the cup. This started her interest in the cup itself. Once she was used to drinking from the cup I just started handing her sippy cups and she took right to them. I think we used the Nuby (wal-mart) soft tops at first.
It just seems to me that the sippy has to be a little confusing. I mean, they get a drink like out of a cup and have to swallow accordingly but yet they still have to suck as if from a bottle. Have you ever drank from all three? I'm the type that has to try everything so I drank from the bottle, sippy, and reg. cup... the bottle forces you to swallow differently then the sippy and the reg. cup (which are more like each other).
Try drinking a few drinks of whatever through the bottle you use and then try through the sippy cups you're going to try and see which cup would seem the most similar to the bottle in gulp size, sucking action needed to get a drink, the way it feels in your mouth, etc. Also, a lot of the spill proof cups have those plastic inserts that prevent spilling but if you have ever tried to drink through them it can be really hard- I take all of those out of Ella's cups, I'd rather deal with the spill then a kid who can't get a drink. That would be as frustrating for your child as giving them a newborn nipple when they're ready for hi-flow. They're not going to mess with it at all if they can't get a good drink.