There are a couple of things to consider.
First, in order to avoid interest charges you generally just need to pay the statement balance before the statement due date. This is your grace period. You don't need to monitor your activity every day and send immediate payments. If you're being really tight with money, you can actually make a little profit by letting your cash sit in an interest bearing account before you pay your credit card before the due date.
Second, credit card interest rates are pretty terrible, and prescribed minimum payments are comically low. If you buy furniture using your credit card you will pay some interest, be sure to pay way more than the minimum payment. You should avoid carrying a balance on a credit card. At 20% interest the approximate monthly interest charge on $1,000 is $16.67.
Third, if you carry a balance on your credit card you lose the interest grace period (the first point above) on new charges. If you buy your couch, and carry the balance, when you buy a soda at 7-11, the soda begins to accrue interest immediately. If you decide to carry a balance on a credit card, stop using that card for new charges. It generally takes two consecutive billing period full balance payments to restore the grace period.
Fourth, to answer your question, using a credit card to carry a balance has no impact on your score. Make your payments on time, don't exceed your limits, keep your utilization reasonable. The credit agencies have no idea if you're carrying a balance or how much interest you're paying.
To Appease the people who think point four needs more words:
Your credit report contains your limit, your reported balance (generally your statement balance), and approximate minimum payment. There is no indication related to whether or not the balance contains a carried balance and/or accrued interest. The mere fact of carrying a balance will not impact your credit score because the credit reporting bureaus don't know you're carrying a balance. Paying interest doesn't help or hurt your score. Obviously if your carried balance and interest charges push your utilization up that will impact your score because of the increased utilization. Make your payments on time, don't exceed your limits, keep your utilization reasonable and your score will be fine.