Marriott and United affinity cards are both VISA cards issued by Chase. There's no reason not to carry both, but be realistic in your expectation of how much credit Chase will extend to a new customer, especially if your expenses will be disproportionate to your verifiable income. I assume you have already checked your FICO score?

Even if Chase issues both cards with adequate credit limits, it's important to always carrry at least one card from another issuer and a different transaction network (i.e. American Express or Mastercard). If there is an authorization system failure (at Chase or at VISA), or if Chase suspects fraud and freezes your accounts, or you simply have a dispute with Chase, you still need to be able to pay.

Also, if your expense reimbursement is late, and you must temporarily carry a balance, you will typically not want to put additional charges on that card for two billing cycles because those new transactions will also be subject to finance charges. (This is an important benefit of Diners Club. It's a charge card, and must be paid in full every month, but if you cannot pay you can transfer the charges to a separate account which accrues finance charges, but new transactions are not affected. American Express charge cards have similar features, but not quite as straightforward.)

Choose a third card that you actually want to use, and make periodic purchases in various cities so that the issuer sees that the account is active and that you travel. Not much benefit to carrying a spare if the transaction is declined because there has been no activity for two years.

I would ask more questions about the employer's expense reimbursement procedure. Do they issue payment for each set of expenses that you submit, or only once a month? If payments are made sporadically try to arrange your cards to have closing dates spread throughout the month to reduce the amount due at any one time. On the other hand, if it's monthly ask when the payments are issued, and try to synchonize your card closing dates so that payment will be due a week or more after you expect to receive the clear funds. If reimbursements are chronically late, update your resume.