from personal use, i've used and still own the Logitech diNovo keyboard and MX Revolution mouse; fully charged the battery on both lasts for days. both are older models and still available, changing their batteries are recommend if they show signs of not holding a good charge.
i'm a sucker for mechanical keyboards, most are wired and can be expensive; currently typing on my Happy Hacking Keyboard Lite2(HHKB).
since you're budget minded, i'm sure you can find something similar to Logitech if it's not your product brand of choice.