Can you still get an ASI in your contract as a 68W? What else should you get in the contract?

ASI's will come after you complete your training. As long as your unit has the funds to send you and slots are available, you're a go. For your contract definitely focus on education benefits (MGIB, MGIB kicker and SLRP) and a bonus. Some of these things may not be available but see what you can get. You can always go to another recruiter if your current one is not working out.