You cannot put money in 2 401k plans in the same year.
Something I found out the hard way because the employer assholes never told me that (they have no incentive to tell you that).

What I ended up doing few years ago (when still a wage slave)was to max out the 401k in the first 2 months. You can do that by setting 99% of your wage to go to 401k. It automatically stops once you hit the limit for 401K that year.

That way you de-risk yourself from having a taxable event with larger income + any signing bonus you might have gotten for your new job this summer!

As for the cash, I suggest you invest in your regular investment account (not IRA or roth) and invest a little more aggressively based on when you think you will retire