Let's talk about sleeping systems!
The two primary components of the sleep system are your sleeping bag and your sleeping pad. A pillow is an optional and less important component that we will touch on briefly.
Sleeping Bag Types - A good rule of thumb is to keep your "big three" (shelter, sleep system, and backpack) below a total weight of 10 lbs. I mention it here so you can keep it in mind while we talk about sleeping bags. Sleeping bags have one of two types of insulation - down or synthetic.
Down - down is light, compresses smaller, is warmer for its weight than synthetic insulation. Down bags will last much longer than synthetic insulated bags. They are also much more expensive. Down is worthless when it is wet, so don't get your sleeping bag wet! That said, a wet synthetic bag is close to worthless too, so I don't see this as a big difference unless you are doing multi-day trips in a very wet climate where your bag will slowly lose loft (how poofy or thick your bag is) over time as it gradually accumulates moisture. In that case, synthetic can be a better choice. I use nothing but down bags and love them, though our kids started out in synthetic bags. You can read more about down bags and my favorite sleeping bags in this post.
Synthetic - these bags will be heavier, bulkier, and pound for pound - won't be as warm as down. They will be more economical, though. You can have a synthetic bag that will be as warm as a down bag, it will just weigh more. I started backpacking with a synthetic bag and it served me well for several years.
Never, ever store your sleeping bag at your house in a compressed state (i.e., in its stuff sack or tightly rolled). That will cause the insulating material (down or synthetic) to get permanently compressed. That means it will not be as warm. I have a dedicated backpacking mini-room/large closet where I store my bags suspended from hangers or in large capacity storage sacks made specifically for that purpose. Other options include laid out under a bed with nothing on them, or up on a shelf with nothing on them.
Sleeping Bag Shapes - The shape and cut of a sleeping bag will have a big effect on how warm they are. Mummy bags are warmer than square bags. Smaller bags are warmer than bigger bags (as long as the small bag still fits you). Ideally, a sleeping bag would just fit your body with no extra room to spare. That is because your body has to heat up more space if you are in a loose or big bag. Think of it like trying to heat a 10,000 square foot mansion with the same heater you use in a 900 square foot apartment. Some people struggle with feeling confined in smaller bags, so be sure to try out several options and find what works for you.
Sleeping Bag Temperature Ratings - The short and sweet on this is don't believe them. The best rating system is to take it outside and sleep in it when you know the temperature. If you sleep warm enough, then that is the rating for you. The rating system has gotten better than it used to be. In the past, companies would just slap a number on a bag. Many companies now use the EN rating system. This is a more scientific and consistent way to rate a sleeping bag, but I personally add about 10 degrees to whatever number they say, but I tend to be on the colder side. In general, women tend to sleep colder than men and the EN system accounts for this. You can learn more about this rating system as well as more about sleeping bags using this link. Note that this is not an endorsement for REI, though they have taken a fair bit of my money over the years. When I buy 3-season sleeping bags for my family, I get bags in the 15 to 20 degree F range.
Sleeping Pads - These have two primary purposes - to keep you warm and to help you sleep more comfortably. Sleeping bag ratings are based on the assumption that you have a good insulating pad under you. If you don't, the ground will slowly steal your body heat all night long. There are two general types of backpacking sleeping pads - closed cell foam and inflatable. Their warmth is rated by an R-value (higher is warmer). I've typically been fine in the summer with something in the 2.5 to 3 range.
Closed cell foam - these are relatively cheap, relatively indestructible, and generally thin. I slept on one of these for years and years and loved it. If you are just getting into backpacking, this is a good place to start. They also double as a sit pad while you are eating lunch. You don't have to worry about popping them.
Inflatable - you need to be careful with these. Many are not insulated, cheap ones leak all night and pop easily. Good ones are relatively expensive, but are very warm, reasonably durable, and more comfy than thinner closed cell foam pads. More info on both options can be found here.
Pillows - I have used a rolled up fleece jacket or my stuff sack with some clothes in it for years. Not as comfy as your super pillow at home, but much more practical. Within the last year or two, I shifted to an inflatable pillow. I really like it, but if I were just getting into backpacking, I would spend my money somewhere else and sleep on a rolled up jacket.
Example - This microadventure is from a trip several years ago in Idaho. We were a bit chilly, so we heated up water, put it in a Nalgene bottle and put that in our sleeping bag. This is a great way to either be toasty warm, or wake up with burning water on you that then proceeds to freeze on you and your sleeping bag. I don't recommend this unless you are extremely careful, vent the hot water several times to relieve pressure before bringing it in the bag, and you are 100% sure your bottle is 100% not going to break or leak. Please skip over this part and focus more on the joy of being snuggled up in your bag while looking out the front door of your tarp at a beautiful sunrise (and then catching a bunch of fish).