Hi and welcome to our site!In general - there is nothing specifically you need to do to start your own business - your spouse may just operate under his own name and his own SSN - and generally - so special registration required.
For federal tax purposes - you will report all business income and expenses - on the schedule C -http://www.irs.gov/pub/irs-pdf/f1040sc.pdfThe net income (after deductions)will be reported on the form 1040 line 12 - http://www.irs.gov/pub/irs-pdf/f1040.pdfIf the business has net income over $400, it may be required to file Schedule SE, Self-Employment Tax and net income is likely self-employment income and 15.3% self-employment tax would be required.Self-employment taxes from schedule SE will go to the form 1040 line 56 - http://www.irs.gov/pub/irs-pdf/f1040.pdf Also - you will deduct half of self-employment taxes on the line 27. Generally - that all you needs for income tax purposes . Please review all possible deductions - that might help to reduce income tax liability.
For unemployment purposes - if your spouse will earn income - means if his business will produce net income - his eligibility for unemployment benefits might be affected - and he is required to report that net income.
Registration might be required if you are selling goods and such sales are subject of sales tax - yes - in this case the business must be registered.
Services which do not involve sales of good are generally not subject of sales tax - and registration is not required.
Also - there are some specific types of activities which require license - for instance attorneys, doctors, sellers of firearms, and some others.
Most small businesses do not require any registration.
However - some local cities might require registration if you run the business out of your home - so you may verify with your local administration.
However - you are never required to register a separate business entity - such as LLC or corporation - that is your choice.
You may review following publications related to sales taxes in Illinois - http://www.revenue.state.il.us/Publications/Pubs/Pub-113.pdf
Specifically - see page 4 - You must register with us as a retailer if you "do business" in Illinois and you sell "tangible personal property" at retail.
Under what circumstances would I be registered as a reseller? You will be registered as a reseller - rather than a retailer - if all of your sales of tangible personal property are nontaxable(i.e., all sales are to exempt buyers or are for resale) and you wish to buy your merchandise tax-free from registered Illinois suppliers.