I'm not usually a Starwood guy but in your case, that looks to be the clear choice. Iirc Marriott silver means a free bottle of water/soda in your room. Not worth it in my opinion. What do you think each chain will represent as far as % of your stays? There are more Hilton and Marriott than there are Starwood properties but if going to major cities, it usually isn't an issue.

I'm not sure which card you meant but the Chase Sapphire is the no annual fee version of the card while the card that everyone else mentioned has an annual fee. The "free" card only has double points on dining and no dividend. However, with all the starpoints that you'll be earning it may not matter much unless you are committed to taking your rewards flights on UA.

If UA is preferred, you'll want an Ultimate Rewards earning card for sure. Keep in mind that the "free" cards can't transfer miles out to Chase's partners so you'd have to store them until you obtained a premium card.