The HASTE sequences are obtained in three planes first. Then you do a axial fat suppressed T2 (or if you see the appendix better in other plane then you can do fat suppressed T2 in that plane). Then you do T1 in and out of phase. The T1 are just make sure there is no hemorrhage or fatty lesion in the pelvis.
The HASTE sequences are T2s, which are obtained with a slice thickness of 4 mm with a gap of 1 mm. Playing with slice thickness and making them thinner will have detrimental effect on image quality. So the 4 mm slice thickness represents a compromise. HASTE sequences take 1 sec per image. So motion should not be a problem (most of the times).
The key sequence would be breath-held T2 with fat suppression. I typically start with axial T2 fat suppressed and then ask the techs to get a coronal if the patient can tolerate it.
You also want to get a 2-D time of flight to distinguish a vessel from a fluid filled appendix.
The entire protocol is breath held. So T1 are not that ugly. All of the sequences are done with NEX of 1 (so it is faster).