I believe in allowance, and I believe in chores. I'm not sure at all about combining them because I think you kind of undermine your goals.
Kids should have age appropriate chores but not necessarily tie them to money. Otherwise, when they don't need or want money, they don't think they have to be cooperative family members. Four year olds have no concept of money and what things cost. They can barely count, so they don't get that 5 nickels = 1 quarter, 4 quarters = a 1 dollar bill, let alone that an item with a price tag of $2.99 is really $3 in price, plus tax. They don't study coinage until elementary school, and while things like 10 stacks of 4 quarters each equals $10 which fills a quarter roll is great for multiplication, but not until 3rd or 4th grade.
And taking a child to the store with her own money turns every trip into a "me me" experience, with every errand having a personal pay-off. It also keeps you from saying "no" to a particular purchase (too much candy, inappropriate toy) because "It's my money, Mommy."
So I'd separate them. And I'd make chores very simple - simple tasks rather than a long sequence. So pick your biggest battles in her room and the common room. Establish storage bins or baskets or designated shelves or dresser drawers for key items. Label each "destination" with a photo or a picture from a magazine or website so that pre-readers can identify where Legos go, where stuffed animals go, where socks and underwear go. If you put shoeboxes or plastic bins in a dresser drawer with a label/photo, a child can learn to put her own laundry away easily. To clean the room, have her start with ONE job - because "clean up your room" is way too general. Have her pick up only her clothing and put the dirty stuff in the hamper, then pick up ONLY her shoes and put them in the closet. When that's done, stop, compliment her, and move on. On the next day, do all the toys in one category - dolls & animals, or puzzles and their pieces. Stop, read a story together. The next day, do two chores in a row in the common area. Once it's clean (even if it takes a week), it will be easier to return it to that state after just one afternoon of playing. Associate chores with having more time with her family to do fun things - the work has to get done, if everyone does a little bit without a lot of time devoted to arguments and excuses, we all get there reward of a family movie or board game or nature walk or trip to the library.
This is a good time to institute a sticker chart as a measure of task completion. After a certain number of stickers are accumulated, there's time for an activity of choice.
Then, totally separately, start teaching about money. If you have a big bucket of change someplace, get those coin sorters from the office supply or discount store, and a bunch of coin wrappers from the bank. Make sorting into a game - separate quarters from dimes etc., then organize into stacks. That teaches that a little bit of money, over time, builds up to a substantial amount when it's not spent - that's a lesson in savings and not giving in to the temptation to buy something just because the money is there.
When our son was about 7, we found a child's bank that helped sort money into 3 categories - spend, save and give. He learned to enjoy a little bit, save up for bigger things and donate to charity. The sections had parental locks on them (at least Save and Give did) - It helps to infuse your family values into the subject of money.
His money came from what he found on the street (no kidding - some people still pick up pennies!), what he got in gifts from Grandma, and what he earned doing special chores above and beyond regular chores. So in your case, I'd do at least a few months of basic, no opting out chores as part of being a responsible family member. Then I'd introduce separate, "above and beyond" chores for money - something other than routine maintenance of her space - maybe raking leaves or sweeping off the porch or sorting things for a garage sale. These are optional chores she can do to earn money. She won't be able to do much at age 4, but you're planting the seed. She may come up with added things she can do - and I think it's great to let her choose "her line of work" as long as it's a job she can do safely based on her age, size, ability to use tools, etc. You don't want her dusting Grandma's crystal and she may be far too small to use a vacuum or a set of hedge clippers, but investing in a child-sized rake or broom is fine even if she's totally inefficient at the actual job. You base the payment on the size & duration of the job - just like real life.