You say "company" but at the scale of business you are proposing do you mean a "sole trader" business i.e. not a limited company. If you propose to go the unincorporated sole trader route then You should register with Revenue on form TR1. You should also register for VAT if you anticipate sales to exceed €75,000 in a 12 month period. It is preferable to register from the outset however you can run the business for a few weeks and then when you register ensure to do so back to the date of commencement. Not all business would have their registrations done at the time they start.
If you are proposing to use a business name which is not your own name then you need to register the business name with the Companies Registration Office Business Names Section on form RBN1. This does not protect the name in any way but is a legal requirment under the Registration of Business Names Act.
If you have other income then any profit from this business would be added as a top slice onto your other income and the profits taxed accordingly at your marginal rate of tax. There may also be PRSI / Income Levy & Health Levy.
Remember expenses incurred wholly and exclusively in the course of the business are deductible in arriving at taxable profit. Some expenses such as computers & other fixed assets are alowed over their useful lives not all in one go straight away.