Infant car seats (the ones you can carry) are WONDERFUL. They don't use them long, though, so if finances are a problem, you can skip it. But I simply couldn't live without one because:
1) You can buckle the baby in inside the house, where it's much easier to fumble with all the straps and buckles.
2) You can carry the baby into places without taking him/her out. This is especially helpful when he/she is sleeping. Which is a lot.
3) You have somewhere to put the baby down. At church or in a restaurant, you just don't want to hold the baby constantly. I'm sure people had other solutions before infant seats (such as Moses baskets?) but now, it seems like everyone uses the car seat.
4) What else would you do with the baby when you're grocery shopping?
I bought an inexpensive travel system when I was expecting our first, and I liked it. That was until my first two babies outgrew the included infant seat in 5 and 4 months, respectively. Then I had to move them to a "big" car seat (they're called convertible car seats). Luckily, they sat up very early, so I could put them in a shopping cart seat soon after they had to stop using the infant seat. Even so, for a while I had to haul the infant seat in the trunk so I'd have somewhere to put the baby while shopping.
I later learned that more expensive car seats have higher height and weight limits. That is totally worth it to me.
And then there's the question of the stroller. I liked the one that came with the travel system fairly well, but they're bigger and bulkier than others you can buy. And strollers last far longer than car seats. I sold our infant seat at a yard sale, and felt like I had to sell the stroller with it because they matched. The car seat was going to expire before I had another baby, so I wanted someone else to get some use from it.
With my 3rd baby, someone gave us a higher height/weigh limit infant seat. Good thing, because baby #3 would be outgrowing our old seat about now, and I'm so glad to still be able to use an infant seat/carrier still.
I think if I'd known what I know now, I would have bought an infant car seat separately from a stroller. Most of the time, we don't click the car seat onto a stroller, anyway. My babies like looking out at the world, not back at me, so they prefer to sit just in the stroller. The only time I can imagine clicking it on is when we've driven somewhere, the baby's asleep and we're going on a walk or to a store without carts. And that just doesn't really happen. Besides, you will use the infant car seat for a few months, and the stroller for years, so get an awesome stroller!
Now, you could keep the car seat that someone gave you, but I think I'd return it. Depending on which infant seat you buy, you'll probably need a convertible car seat when the baby is about 6 months old. But I learned the hard way that these seats have expiration dates, so it really does matter when you purchase it! There is a date stamped on the back or bottom of every car seat, and you need to throw it away when it reaches that date. Even when the seat is sitting in your closet, the clock is still ticking on it's expiration! I would return it, put the money aside, and repurchase it when you need it. Chances are you'll get a seat that was manufactured months later, giving you longer to use it.
I learned this when I bought a car seat on clearance. Don't do that! I didn't even think about it, but when I opened the box and looked at the expiration date, it was only 5 years away. It had wasted a whole year uselessly sitting on on a warehouse shelf. And I only saved $15 on the thing!
As for strollers, I loved going to Baby Depot inside Burlington Coat Factory to test them out. They have floor models that you can "test drive" around the store. Be sure to fold them up and lift them and imagine hefting it into the trunk of your car. Most stores just have boxes to look at.
Hope that helps!
P.S. I just read down a ways in the comments and you should NEVER EVER NEVER turn an infant seat forward-facing! And infants shouldn't be forward facing under one year anyway.