I think this is tricky, because it's a skill between two separate skills handwriting (letters) and drawing.
I have pretty bad hand writing, but I studied art in college and could draw pretty well.
Drawing straight lines is actually difficult!
Two things that might help:
If you hunch over to get your eyes close to the paper, move back so you see more of the full page in your center of vision. If you see more of the page edge, it can help to get your lines straight.
When drawing lines try using you elbow and shoulder more rather than your fingers and wrist. That should give you less curving motion and therefore straighter lines.
For consistency don't just write from left to right. Sketch proportially across the whole page. I try to first make equally spaced bars. First mark a bar in the middle then start adding bars splitting into quarters, etc...
Mark the first note head with just a light dash. I think getting the first beat placed consistently is more important that whether the last note head has more or less space at the end of the bar. After the first beats are set then add the other noteheads as light dashes...
After you have lightly marked noteheads, you might make quick adjustments for anything that's badly aligned. Then draw stems. Sometimes I have drawn stems from the note head so I don't have to worry about getting the line connected to the head...
When the light sketch looks good finally fill in the note heads - or just bold ovals for half and whole notes, cross the stems with beams, etc. If the note heads are a little smaller that a staff space, it should help make clear when it is on a line or space (note heads on spaces won't be touching lines.)
Basically the idea is mark out important spacing points across the page first then make the bold marks over those guide lines. I think if the spacing is consistent and proportional, then the final result is easier to read.