We approached the transition from formula to cow's milk and bottles to cups as completely separate. You might find it's no big deal to do both at the same time, but we found that ours wasn't ready for milk from a cup at 10 months which was when we first started to occasionally offer small amounts of cow's milk. So we didn't push it and just stuck with the bottles. She happily switched to a cup around 13 months, which worked great. There's no rush to do either so I would pick the one that seems the easiest if at first it seems like too much change and focus on that first.
We started to offer small amounts of cow's milk in a bottle with an afternoon snack at about 10.5 months. So it didn't really replace a bottle as she'd dropped that bottle for a snack, but it was just a way to start introducing a little bit of pure cow's milk so she could get used to it. From 11 months, I switched out 1 bottle per day each week. So she was having 4 bottles a day at 11 months, so 3 of them were formula and 1 was cow's milk. Then the following week, 2 were formula and 2 were milk. We switched completely to cow's milk at 12 months. That worked well for us. She did have a bit of tummy upset and loose stools, but she was teething at the same time, so no idea what really caused it. It was fine after a couple weeks (also when the teeth popped through).
For switching to cups, I just periodically offered milk in a cup from about 9 months. She might have a few sips but mostly completely refused it. At around 13 months, I offered it one morning (in a straw cup, not a beaker) and she took it happily. After that, we switched all her daytime milk to cups (morning and afternoon milks). I kept the bedtime one in a bottle as she was usually very sleepy and I didn't feel like she was quite ready to manage a cup for bedtimes yet. At 15 months, I switched the bedtime bottle over to a cup and it was fine. I think just taking your time with both transitions is key and if it's really not working, don't push it and make it stressful. Give it a few weeks and try again.