Depends what you mean by budget. You can get old Vista, Windows 7 or even XP laptops on Craigslist or EBay for fairly cheap.
If, like most people, you want a newer budget laptop, I would suggest you go with a Dell, HP, etc. refurbished/off lease. I have only had experience with Dell. Always been more than satisfied. And, at times they run sales, even on the refurbished.
Got my college student son a fantastic deal on an off-lease Dell laptop this summer. With a 50 percent off sale, snagged with for $165. Don't remember all the details, but it was NOT a stripped down model. Indeed, it has lots of memory, etc., quick processor and has Windows 10. I was able to install Office 2016 for free on it, so it was a fantastic find (he had spilled coffee on his other machine, a fatal error).
As I said, I am not pushing Dell, it is just the site I have used and I have purchase three different laptops from them.
HP and the rest also have deals. Woot sometimes offers fantastic prices, you can check their web site, but they are a little different (owned by
Amazon). If they have something today, they WILL sell out of it by "tomorrow (sort of)>" Check woot out if you have never seen them before.
O.K., to be nice, here is the current Woot laptops page. looks like mostly HP, which has been my experience with Woot. My current desktop is from Woot (an HP) and it is a fantastic machine, which I got for $280 or so a year ago
http://www.woot.com/category/computers/laptops?ref=w_cnt_cdet_pc_3
Also, try Techbargains.com....look for laptop deals. Luck!
Whew, looks like Dell is having a 55 percent off sale on refurbs that ends on Sunday, you might want to get there quick....the good stuff goes fast....
Remember the price you see on the Dell page is BEFORE you add the code you see on the Techbargains page. The code will bring the price down significantly from what you see on the Dell page.
https://www.techbargains.com/dell-financial-services-weekend-sale