I was absolutely bricking it when teething time came around, as there's all this pressure to puree your own food, give healthy stuff constantly etc. Pfft.
Here's what I did:
Pureed veg and fruit for an entire month and was utterly miserable and exhausted doing so. Baby didn't seem to care about the difference but I was wasting time making food that I should have spent with her.
So after a month we started buying Stage 1 pouches from the store, all pureed, all healthy. She started off only having a few spoonfuls per meal of it, then I'd give her a snack to nibble on (baby crisps/wafers etc, find in the baby food aisle). I also started offering her soft foods like a banana, or some bread, raspberries etc; anything she could mush up/make a mess with. Because she was getting pouched food, I didn't worry that she didn't really eat the real food.
Once she could finish a whole pouch per meal and still want more, I started trying to give her the 7+ jars of baby food, as THOSE encourage them to chew (babies don't need to learn to chew at 6 months, whatever HV says, they'll learn within the first year when they're ready). She's still have pouches sometimes, and more solid foods like a piece of ham or breadstick. If your baby can't munch it up, they won't. Simple. No harm offering. Offering food allows them to learn HOW to get it to their mouths on their own.
My lo has a smaller appetite than many babies, and she doesn't like to feed herself, she much prefers I feed her with a spoon, whereas your baby might well want to feed themselves. Just try different things and prepare for it to all be messy.
As for whether store-bought food is okay for your baby, it is pretty much all organic now and HAS to be safe. Asda do amazing deals on jars and Aldi pureed pouches are unbeatable on price. It's all safe for babies to eat, and all baby snacks (Stage 1 or 6+ months) will melt in their mouths.
If they seem to be coughing when eating then it is just them learning to swallow thicker foods than milk, and offer them water if it's dry food. Babies will eat anything you put in front of them, usually. Also, it can take up to 10 tries for a baby to decide whether or not they like something, so don't give in!
It's scary trying something so new and MESSY, but it can be great fun watching their eyes light up at a jar of spinach you wouldn't dare touch, and gobbling it down!