I currently just graduated and received a job! Wahoo! My Dad told me he is still going to claim me though, for this year anyways. First question is: What does that really mean? Also, should I claim a 1 or a 2. I would like the most money I could get right away without having to pay in. Does him claiming me make me get less money back? I am only 21 years old and went to school for the first semester of the year.
Assuming you're in the USA, here goes:
In 2018, this is a very different boat than in 2017 and before. Before, there was a personal exemption of $4000 that you didn't get if someone else claimed you, and instead they got you.
But in 2018, that doesn't exist - so your dad is wrong. He won't claim you, because there's no exemption to claim. (See for example this article.)
Ultimately, you are best served filling out the W4 according to the instructions for your first year. Then figure out at tax time next year if you're over-withholding or under, and adjust accordingly.
My guess is you'll enter a '2', if you're single and have one job and no kids.