Chase Freedom is a really good beginner card, if you can manage to get it. I was preapproved for one through our local Chase (since our family has banked there for many, many years) so I haven't had to deal with the application issues I see some other reviewers have, but I've personally had almost no issues with either how the card works or the customer service.
I've had mine since 2013, starting with a credit limit of $1,000.00 and have increased the limit to (and kept it at) $4,000.00 because I'm not a big spender or moneymaker. The points system can be a little tricky to navigate (because of the rotating bonus 5% back categories), but I think it's fairly decent - each year I've had it, there will be one quarter with 5% back on gas stations and one with 5% back on groceries, which is higher than for the other cards I have. I also use the Costco-partnered AmEx, so I just end up rotating between the two cards depending on which has the higher point reward at the time.
n addition, Chase will alert you to suspicious/questionable charges. Somebody tried to put ~$160.00 on my card last year, and Chase got an email to me about ten minutes after the charge was made asking whether it was a charge I had made or not. Literally all I had to do was click "No" on the email for Chase to decline the purchase; they then directed me to call a specific customer help line, which was answered within 2 minutes (I was calling at around 6:00 PM, when I finally got off work) and had a very nice representative walk me through cancelling my card and sending me a new one, which got to me within two weeks.