it of course depends on what parts you buy and from where . i had £400 in a rear wheel years ago but you could pick something up for a tenner much like mtbs
am i right in guessing your of average height ? 5.10 ish ? look for a frame between 20.5-21 toptube . unless its really old , bikes back then had very short toptubes
frame-
forks- either 1" or 1.1/8" depending on frame . 10mm or 14mm depending on what hub
headset - again inch or inch eighth
stem-ahead for eighth or quill for inch . all around 55mm
bars- go for around 8"
seatpost- will likely be 25.4 or if its older 22.2
cranks- 3piece , profiles keep their value . i use prolites which cost £70 new and are near enough copies of primos
bottombracket- american size most likely
front wheel - 48 or 36 spoke . 10mm or 14mm axle
rear wheel - likely to be 14mm if the frame has 14mm slots . if the frame has chainstay ad mounts for the brake you might not be able to fit a chainring larger than 44t-16 without the chain rubbing the brake . if the brake is on the seatstay you could have whatever gearing you like . 44-16 , 39-14 a 14t freewheel requires a flip flop hub unless you get a cassette hub . old cassette hubs will almost certainly have had a hard life . odyssey makes a 13t freewheel that fits a flip flop hub and gives 36-13 . below 12t on the cassette and it turns into dedicated drivers where the sprocket is part of the freehub body , these go as low as 8t
chain- 3/32 is race . 1/8 is normal . 3/16 was a point in time where we used scooter chains , best left to the past
brake- called ad990 after the ubiquitous dia comp brake that uses stud pads ( like a canti ) there is also a hombre that is the same except for V type pads . you could pay from £10 - £80 for a brake . a £10 hombre will be fine . if the frame is older and lacks the posts itl be a caliper brake
the rest is all fairly obvious and standard bicycle size
i have an old diamond back frame painted red you can have for nowt . quite heavy