This list is for the South Dakota Rapid City Mission. Other missions may have some different requirements but for the most part I think this list will be generally close for most missions. If you are curious what is needed, here you go.
Read any packets you receive completely
Complete the acceptance letter!!! This can be done online.
Complete any medications and medical procedures.
All medical things must be resolved.
Record immunizations online.
Fill out flight ticket if flying to MTC.
Setup Shuttle - Salt Lake airport to Provo
Setup and check email regularly at myldsmail.net
Before entering the MTC
Do online missionary assignments that are waiting for you.
Get your Temple Recommend and stay worthy to enter the Temple.
Read the Book of Mormon daily.
Be familiar with Preach My Gospel chapter 3.
Watch the videos "The District 2"
Create a Mormon.Org profile
Learn about your Family History
Make a copy of your Patriarchal Blessing
Resolve ALL worthiness issues.
Settle ALL Debts.
Put name on ALL luggage, clothes, and belongings
Have hair cut according to missionary grooming standards.
Continue private health care and bring medical card with you.
Be set-apart as a fulltime missionary by Stake President.
Realize your assignment could be modified.
Receive a father's blessing.
Reporting to the Missionary Training Center
Dress as a missionary.
Report time will be given 4 weeks before report date.
Farewells should be at home.
Bring completed Immunization card.
Bring a gov't issued ID
Bring Temple Recommend
Bring a four generation pedigree sheet
Bring stories about your ancestors.
Bring a journal
suggest bringing pens, pencils, notebook, highlighters.
A non-logo shoulder bag, conservative style.
Optional MTC approved books.
2 bath Towels
2 hand towels
2 wash clothes
Set of twin sheets - zipper type for bed bugs.
Shaving kit bag
Shoe polish and supplies
First Aid kit with meds
Small sewing Kit
1 lrg suitcase.
1 med suitcase
1 Carry-on / Messenger type bag.
Learn these things
How to cook basic meals
How to sew buttons, mend
Get in a habit of waking up at 6:30AM and going to bed at 10:30PM
Learn good manners, especially at dinner.
Learn to set daily goals.
Setup bank account with debit card.
Make sure bank account has at least $200 + money for a bike.
Make a $400 Payment to Missionary account one month before you leave.
Carry a little cash for snacks and such around $50
Medical ID card
Leave written authorization w/ parents
If bringing meds, leave them in their original containers
Bring insect repellent
10 White Shirts
10 Pair Garments
2 Thermal Garments
2 Pair of shoes.
1 Winter Boots
Service Project Attire
Cold Weather coat jacket with liner
Cold weather ear protection
1 Shower slippers
So there you have it! I'm sure there are other things that could be included. And some of these things will be different for other missions but most will apply. Obviously, this is a list for an Elder, not a sister.
One tip, if possible check with those who have served in the same mission or are serving in the mission now to see what things could be bought there. That will save room in traveling to your Mission.
Now to get all these things ready and figure out how to pack it in the suitcases. All fun!