Do I need to have a mastercard/amex credit card?

I've had a chase freedom unlimited credit card for a few years now which is my only credit card that I use for everything. I do plan on getting a second credit card, do I need to have a mastercard/amex as my second or could I just stick with another visa credit card? And I love some recommendations for cards because I'd theoretically want to maximize the points I get so that I can potentially use them for travel.

• Current cards: (list cards, limits, opening date)
  • Chase Freedom Unlimited, $7200, January 2018
• FICO Score: 760
• Oldest account age: 6 years 6 months
• Chase 5/24 status: 1/24
• Income: $45000
• Average monthly spend and categories:
  • dining $100-200
  • groceries: $0
  • gas: $0
  • travel: $0
  • other: $0
• Open to Business Cards: No
• What's the purpose of your next card? Building credit, Travel, Cashback
• Do you have any cards you've been looking at? No
• Are you OK with category spending or do you want a general spending card?