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If you start with the Starter Set, you don't need anything other than the starter set. No DMG, no MM, no PHB. I'd recommend the PHB if your friends are the type who would be interested in creating their own haracters, but you don't need the rest.

The starting set comes with an adventure for you to play through, a copy of the basic rules that tells you how to play, the information for all the monsters in the adventure (and information on their personalities and how to play them), and blank character sheets as well.

You'll need sets of polyhedral gaming dice, and you can probably get a Chessex set from any gaming store or a lot of toy stores, but of course you can order online. Tip: try to make sure you and your friends all get your own sets, and try not to get the same colour.

And that's all you need. There are other things, which are optional, but they're also cheap so they're worth mentioning.

It is entirely optional to play on a grid; you can do "theatre of the mind" where you describe what happens and the players describe their actions and movement. It's also possible to play on a 1" grid; office supply stores will sell giant pads of grid paper with a 1" grid (I think mine is 28"x34" or somewhere in that ballpark). This is the same stuff you used in high school, but huge. Personally, I find this easier because I don't have to try to keep the whole battlefield in my head, but it's not necessary.

If you do go for the grid paper thing, you'll want tokens to represent your characters. We bought this set, they're close enough for most characters and you can order custom ones from Heroforge if you get really into it. You'll also need tokens to represent enemies; we use glass beads and it works fine. You'll want a pack of markers to draw on the grid paper too.

The other thing I'd recommend is a notebook, and 3"x5" index cards just come in super handy; for example, my players are fastidious about making notes when they get sent on a quest so I write down the salient details on a card so they don't have to (just to save time) until I've got the hang of things. Same with handing out magic items; write it all down on a card, hand it out when the player finds a card (after you tell them, narrative is important!).

Lastly, prep your session ahead of time. You don't have to do much prep, but if you're doing something like Lost Mine of Phandelver (from the starter set), read trough the next part to see what kinds of things are going to happen, what kinds of loot you'll find, etc. That will give you a chance to change things up (for example, to change a +1 longsword into something else if no one in your party uses a long sword). I've had a few sessions where I got tripped up because I got blindsided by The Adventure as a direct result of missing a paragraph in the adventure we were playing, which left me scrambling.

Hope this helps.

TL;DR don't buy the monster manual or DMG yet, maybe buy the PHB, but definitely buy the starter set and some dice.