If your solvents are completely miscible (and do not react with each other) then this will not affect the mixing of your two materials.

The best thing to do is to do a test-mixture of your two solvents first, without your materials in and check if you can see a phase boundary.

Most polar solvents (particularly those containing oxygen, e.g. alcohols, ketones) are completely miscible with each other, and with water

Something to think about - if you want to remove the solvents from your mixture afterwards (for example via distillation) then think carefully about the vapour pressures and boiling points of your two solvents. If one solvent has a very high boiling point and low vapour pressure compared to the other one, then you could end up with solvent residues of the high-boiling-point species because it will be more difficult to remove.

If you do a web search for "solvent miscibility tables" there is useful information to help you (such as https://www.csustan.edu/sites/default/files/groups/Chemistry/Drake/documents/solvent_miscibility_table.pdf)

Does using different solvents effect the miscibility?

Yes it does.

For an example solvents can be polar protic (Having hydroxyl groups), polar aprotic (polar but no hydroxyl groups) and non polar solvents like hexane, pentane. You may have heard the term 'degree of solubility' which depends on the type of the solvent on the material.

You can see if you can dissolve in those solvents and conclude which one dissolves which.

Hope by doing that you'll get to know the miscibility of the materials.

The two solvents should be compatible. There are solvent charts for maximum percentage of a particular solvent into another. You need the maximum solubility in each solvent and your target concentrations. In addition, if it is not enough, use a third one.