I am a man. I need long fingernails for the job I have- just thumb and pointer finger. It is fiddly manual work- they provide tools but often my hands aren't good enough to use those tools effectively. I also do some private tutoring and I need for my fingernails not to look dirty. How can I achieve that look- hopefully cheaply? The tips develop an off-white somewhat yellow look and grey at the corner.
You may be worrying too much about this. The white tip on a fingernail is the natural state of a fingernail. Everyone's fingernails look like this. Nobody will think yours look 'unprofessional'.
Conversely, if you modify your fingernails to make the tip not look white it'll attract attention as they won't look natural.
In case your fingernails are still dirty after washing your hands, you can use some tissue to help clean them (wet and soaped), or wet wipes. If you are using something like ink or grease your fingernails may get stained, and as far as I know there isn't much you can do about it (but that's stain, not dirt, and it's part of the job; I wouldn't be worried about it.)
Otherwise, (unless that would interfere with your work) you can use disposable gloves to prevent your hands and fingernails from getting dirty.
To avoid having those two fingernails stand out, keep all your nails at 1 to 2 mm all the time. (Using a nail file once a week or so.)
That way the two slightly longer nails do not stand out as much as they would if the rest of the nails are kept very short.
This length of nail can easily get dirty, so cleaning your nails before and after each meal as well as every time you need to wash your hands while working or tutoring is a good habit.
The tip of a file is often kept plain for use to clean nails.