Call it what you like and dependant on where you are it might well be a storm cellar or be used as a safe room but it amounts to the same thing.
There are many forms. Fibreglass, free standing, solid steel, made from drain culverts but it usually tales the form - at least when we think of a typical one - of a 50's Atom shelter.
One idea, using shipping container design as the basis is so-called 'blast resistant buildings' or modules.
As I say make the best of what you have and within your budget. Oh, one final aside: do not make your doors so thick (5 feet) or heavy (350 ton) that they take a whole 24 hours to close as per a certain Swiss tunnel cum shelter. A tad too much me thinks.
Using a potential property I may be about to purchase I have either a cellar (I'm not sure it has one), an under patio option (possible but too close to the house if it was knocked over) or under a nearby outbuilding. It has a HUGE hill close by which affords some natural protection - if only from potential blasts. Ideally I'd own a patch of land half way up and dig in.
Let's argue that I go under the patio (so entry is outside the house). I'll not have much to play with - say the width of the house less wall by the depth of the patio. At a guess 12 x 12. Allow for wall thickness and you're looking at 10 x 10. Not exactly perfect but more than enough to store and secure.