The federal funds rate is one of the risk-free short-term rates in the economy. We often think of fixed income securities as paying this rate plus some premia associated with risk.
For a treasury security, we can think this way:
(interest rate) = (fed funds rate) + (term premium)
The term premium is a bit extra the bond pays because if you hold a long term bond, you are exposed to interest rate risk, which is the risk that rates will generally rise after you buy, making your bond worth less. The relation is more complex if people have expectations of future rate moves, but this is the general idea. Anyway, generally speaking, longer term bonds are exposed to more interest rate risk, so they pay more, on average.
For a corporate bond, we think this way:
(interest rate) = (fed funds rate) + (term premium) + (default premium)
where the default premium is some extra that the bond must pay to compensate the holder for default risk, which is the risk that the bond defaults or loses value as the company's prospects fall.
You can see that corporate and government bonds are affected the same way (approximately, this is all hand-waving) by changes in the fed funds rate.
Now, that all refers to the rates on new bonds. After a bond is issued, its value falls if rates rise because new bonds are relatively more attractive. Its value rises if rates on new bonds falls. So if there is an unexpected rise in the fed funds rate and you are holding a bond, you will be sad, especially if it is a long term bond (doesn't matter if it's corporate or government). Ask yourself, though, whether an increase in fed funds will be unexpected at this point. If the increase was expected, it will already be priced in. Are you more of an expert than the folks on wall-street at predicting interest rate changes? If not, it might not make sense to make decisions based on your belief about where rates are going. Just saying.
Brick points out that treasuries are tax advantaged. That is, you don't have to pay state income tax on them (but you do pay federal). If you live in a state where this is true, this may matter to you a little bit. They also pay unnaturally little because they are convenient for use as a cash substitute in transactions and margining ("convenience yield"). In general, treasuries just don't pay much. Young folk like you tend to buy corporate bonds instead, so they can make money on the default and term premia.