Running a business is an animal all its own. I'm currently doing the same thing you are: consistent nice paycheck from full time work, but doing consulting on the side. I also run some non-consulting side businesses as well.
A lot of the taxation, salary, and business-form questions are answered by the type of work you are doing, exposure to risk while doing it, and your expectations of income. Before I go further, I'm not a business attorney (though I'm married to one) nor am I a CPA. Take it with a grain of salt....
For your formation, you have a few options. Beyond a sole proprietorship (which I'm guessing is what you're doing now) the two logical options are an S-corporation or an LLC (there are also C corps but those aren't generally for small businesses). S-corporations are federally defined and thus consistent state to state, while LLCs are defined on a by-state basis so the fees and requirements in your area may be different from mine. Both of these forms limit your liability in case of lawsuit to the assets of the company. They protect your personal belongings from being liquidated in a suit, assuming you operate in good faith. There are fees associated with this; typically you need to file an annual report and pay for the privilege. I am in MA, and an LLC requires a ~$500/yr filing fee (one of the most expensive states). Part of that decision depends on what you have in the way of personal assets. If you own a home, it should be protected by a "Declaration of Homestead" which means up to a certain dollar amount your home can't be seized as a result of a lawsuit. Other property, up for grabs. Your tolerance for risk should play a part in whether or not those fees are "worth it" to you. How much do you think you'll make on your side business? If you're running a casual, no-marketing, take-projects-when-they-land-in-your-lap kind of thing, it might not be worth it. If you expect to make 10+ thousand, I'd seriously consider incorporating.
For both of those business vehicles taxes "flow through" to your personal tax return. That means whether the money is in your company account or yours, you get taxed on it. Your business is allowed to write off many more things than you are personally, so many times people choose to put some expenses (phone, home office, some mileage, etc) on their business to help with taxes. Some are more aggressive than others on what they call business expenses. "Entertainment" like meals out and tickets for sporting events can be argued as business expenses if they are for a business purpose, but the IRS only allows you to take 50% as a write-off.
I recommend keeping accounts separate and writing yourself checks to keep the books neat and orderly. Co-mingling funds is generally a no-no from an accounting perspective. It's easy enough to do an online transfer and record what it was for. Either way, if you pay yourself say 25k in salary, and have 10k left in your company account, you'll be taxed on 35k of business income less write-offs.
I don't want to give too much in the way of tax advice because I'm not a CPA; do it by the book. That being said, I couldn't imagine life without some sort of business to help with tax planning. You can do many of the same things tax wise as a sole proprietorship as an LLC.
Beyond the limited liability offered by your corporate form, you may also look into errors and omissions insurance and general business liability insurance. I tried to avoid these as long as possible because I despise insurance and keep few assets within my company, but some larger companies simply require it to do business with you. I do a good amount of university work and they are always full of byzantine requirements. My E&O only runs about $35/mo and I was able to get rid of general liability as I work remotely.
I wish you tons of luck with your small business. I also look forward to reading everyone else's advice.
Eric