I use my credit card almost exclusively. I
hate using cash -- it just kind of disappears here and there with no record of it. On my CC, I have a record of it even if I forget to write it down when I spend it. I use an AmEx Blue card, which doesn't have an annual fee but still has a lot of the protections and rewards of AmEx. I use it for 90% of my transactions, and I use the rewards either to splurge on something for me or to buy Christmas gifts at the end of the year. (I can use the reward points directly as cash on Amazon, which is
awesome.) I have a backup Visa that I've had since college. That kind of long-term card gives a nice boost to your credit history, and it's important to have a backup since not everyone takes AmEx. I usually keep no more than $20 cash on me and use it for incidentals -- buying a lottery ticket and a coke when I get gas or something like that.
I figure using credit card only makes the most sense, as long as you are disciplined enough to only spend your budget. If cash is stolen, it's just gone. If I use my debit or CC, I'm only liable for a small amount. But with the debit card, the money is gone from my account immediately and might take time to get back, so I might not be able to do my usual spending while I do that. With the CC, I'm totally protected. Plus, if I ever have a dispute with a merchant, I can unleash the ravening hordes of AmEx on them.

That scares them a LOT more than just me getting mad. With that and the rewards, I'm basically getting paid to spend money in a more secure way. Definitely a win-win.
For budgeting, I have an app called EEBA. It basically has a bunch of "envelopes" that you put virtual cash in. I have them for things like Groceries, Gas, Bills (the ones that get auto-charged to my CC), and Fun Money. I have it set up so the budget month starts on the day my new CC statement starts, and I fill the envelopes to the budgeted amount. Every purchase on my CC, I enter it into the appropriate envelope. It's made a huge difference for me on budgeting! (And it's a free app.

)
The only thing I save cash for is when I'm saving up for a vacation or something. I save up money as I get a little extra throughout the year and tuck it in an envelope. When it's time for vacation, however much I've saved is my spending money. No using the CC except for something like the hotel, which is pre-budgeted.