I recommend one of two options.
(1) If your local taxes don't bother you and you don't have issues with your employer for doing consultancy on the side and you can manage costs of having a local company, then do a local company. Type of company will depend on your long term plans, will change your costs and also taxes.
(2) If you want to manage your taxes, have long term plan to save some money, keep money in business to be able to invest in growth, and costs/taxes in your Country of Residence are too high, you can set up a company in a favorable environment. European tax laws are pretty solid, so any money you put into your pocket while residing in your home country will be taxed in locally ( I am assuming you are planning to be legal and transparent). If you find a partner you can work with in the long run, and you get visibility over your costs, taxes etc. you can work through a company in a different country. What can you get?
- A low cost low tax business environment
- Control over how you get money in your pocket, meaning control over your taxes
- Ability to use lower tax income methods in your own country
- Ability to get the money you accumulated in the company when you change residence to a low-tax/no-tax country in a year. For example you worked for 5 years like this, and kept 20K per year in the company. You have 100K total, which will be taxed locally when you take it out. If you move to a low tax place (may be same country of your company or a different country) you can take all the 100K out with low taxes. Your country of citizenship will not tax income if you are not a resident (unless you are USA citizen of perm. resident).
If you just do this on your own, the tax laws of your country will require you to pay taxes on your offshore income too. You need the correct company structure and tax plan. For this you need a proper partner. I know of one that does this for 3600 USD a year that includes all costs except taxes. Taxes depend on the consultancy topic, may be 0% or 15%.