The choice of stock solution concentration depends on a various factors.
What is the solvent? If the solvent needs to be kept to a minimum in the experiment, then make the stock solution as concentrated as possible. On the other hand, if you can dissolve the substance in the same solution that will be used for the experiment, you may not need to make the stock solution highly concentrated compared to the concentration you will ultimately be using.
How soluble is the substance in the solvent used to make the stock solution? The substance should be completely dissolved in the stock, if possible, although suspensions can sometimes be used if they are homogeneous, as long as the undissolved substance dissolves when the stock solution is diluted.
What is your capability for accurately weighing the pure substance? If you don't have a balance capable of accurately weighing very small amounts, it may be desirable to make a concentrated stock solution to avoid having to make an inconveniently large volume of a less concentrated one.
In theory it should be fine, but you could run into a few problems such as those listed below:-
1) The protein in question may not be that soluble.
2) A protein solution of 10 mg/mL may be very viscous and thus difficult to pipette accurately, with a significant proportion remaining in the pipette tip as a thin film.
3) Problems pipetting accurately due to stable bubble formation, although high speed centrifugation will usually collapse the bubbles.
4) Formation of insoluble or gelatinous aggregates on standing, and thus the concentration in solution may not be uniform.
You may dilute to 1mg/mL from the stock (10mg/mL), it is 1:10 dilution. It is better not pipette a volume of stock less than 10uL. That means you may add 10uL stock into 90uL to make 1mg/mL solution.
And then it is easy to dilute to 0.5 or 0.1mg/mL from 1mg/mL solution.
If the stock is viscous, be careful of the pipetting and make sure to be accurate.