Pram would be fine for daytime naps. Or a bouncy chair if you have one. The change needed for daytime naps is that baby sleeps independently of you (So not on you or in your arms) and isn't fed to sleep.
As to where to start: I'll take your wish to sleep train quickly as a priority over how much distress is caused (this may not be your prorities, you need a good think about what is your priority here).
Move your feeds away from sleep time. So at bedtime feed at the start of bedtime routine not the end. For example feed downstairs on the sofa and then have a bath/wash into night clothes and bedtime. For daytime naps feed when waking up, not going to sleep. So baby goes in the pram/bouncer/cot awake and not fed.
For daytime - Use movement of the bouncer/pram to get baby to sleep. If possible slow and stop the movement once asleep. Restart movement when first stirring to try and lengthen the nap. Also limit awake time in the day (awake window wants to be around double nap length) to avoid baby getting over tired and making getting to sleep harder.
At night, move the full sized cot into your room and remove one side. Put baby into cot awake, ideally with a dummy, having been fed earlier and well winded but awake.
Physically have your torso in the cot. One arm holding both of baby's hands in yours on baby's stomach area (This is to stop arms flaying around). Other arm either encircling baby's head or if you get lots of leg kicking, arm on baby's legs to still them while in the cuddle.
Baby will cry. A lot. Be caring and compassionate about it. But keep going. Cuddling, have your face close to baby's, shushing and white noise may help. Keep on cuddling, keep going through the tears until baby goes to sleep in the cot.
Remember your baby doesn't know how to do this without sucking, so don't get frustrated that it takes a long time with lots of crying. It will, this is to be fully expected.
What's important is that you don't "waste" the distress you cause. If you've gone through all of that distress at bedtime, then don't confine through the night, then there is no reason for that initial distress in the first place.
So at night, try to resettle without feeding (Ideally with a dummy) and start thinking about limiting night feeds and moving all calories to the daytime so none are needed at night. You could night wean. If you have to feed then obviously do. But feed sitting up and try to keep baby awake. Unlatch before baby us asleep and move baby upright on your shoulder to wind. This should rouse enough so baby isn't asleep when being put in cot. Then do your same in-cot settling to get her to sleep, even if crying.