Personally, I never consider anything complete unless I hear it on several very different systems that I am familiar with.
And that means at least once on the car system (it's full-range and can highlight overlooked flaws)
Mastering to 'phones alone isn't really possible because the bottom end is always rolled off
Small desk monitors will have the same issue.
If no option for "big" monitors, use a spectrum analyser and watch what's happening under 240Hz
Remember that low frequencies can produce uniquely rich harmonics as formant objects resonate in a recorded space. (boomtown)
Play what you've completed on a system capable reproducing lows, even if highly colored, just to "know" what's going on.
There's always Beatlephones:
OK, but seriously, on a budget? Either of these will not break the bank, and are quite neutral
AKG K240
Samson SR850