I don't get why you try to relate DPI to lag? They are totally unrelated at all.

If you want it cheap, an entry Logitech office keyboard is one of the best keyboard around for their price, solid and durable.

For mouse, it's more on the ergonomic of the mouse shape. Claw grip vs palm grip. Ambidextrous vs ergonomic for right handers.

DPI had nothing to do with lag. It deters how fast your mouse is moving on a given screen resolution. If you are on multi monitor 4k setup, you won't want to use a 800dpi mouse which will need you drag your mouse over your whole table just to move the cursor by a little.

TL;DR, get a cheap Logitech office keyboard, they can be as good as those so called "gaming" keyboard. Mechanical keyboard can give you a more solid feel, but they are pretty much out of your reach. For mice, take a look at Razer/Corsair/Logitech/Steelseries and get whatever fit in your budget and palm nicely.