This is a big topic and I will only say a few words at present. To begin with the so-called "rental" wheelchairs, provided by medicare/medicaid are totally unacceptable for taking a person outside. They have very hard non-resilient wheels, for one. They are designed for indoor use on smooth hard surfaces, such as in a nursing home. The provider, who is usually a salesman, gives you what they have in stock. These salesman also usually have great bargains on bridges in Brooklyn. This is usually two types or sizes. The wheelchair rental racket is a scam. Just a personal opinion. Obtaining a custom comfortable wheelchair will be the best investment you could make.
Purchase one. Even if the insurance pays for a rental you end up with a Faustian bargain. They never tell you that wheelchairs come in a number of sizes (amazing), heights, wheel types, and the push-handles come at varying heights above the ground.
You ideally need two (count-em) wheelchairs. A small four-wheeled (small wheels) chair for inside the house, with brakes that can be set by the caregiver, and an out-door chair. The foot activated brakes tend to be secured by bolts that loosen and then the health-care aid will vacuum them up and the chair won't have brakes. For some reason the brake supports seem difficult to order from the manufacturer if they fall off. There are several small pieces. . Tighten the bolts that secure the brakes when you get the chair, or better yet, apply some lock-tight to the bolts and re-tighten. These may be Phillip's (the "x" kind) or tightened by an Allen wrench. The appropriate Allen wrench should run you about a dollar. When you roll the four-wheeled chair to a table, the brakes are set so it doesn't move away when the patient pushes on the table or moves while eating.
An outdoor chair must have a soft tire. These tires come in two types. Inflatable (like bicycle wheels) and foam (semi-solid). If you want to see the difference have someone push you around for an hour in the streets in a hard-wheeled chair and then try the ones with resilient tires. In some cases resilient tires can be added to a rental wheelchair.
You will also need a foam cushion for the seat of both chairs. A thin cushion for the four-wheeled indoor chair and a thick one for the outdoor chair. These are available at medical supply stores.
Now you need the leg extensions, of course, but you need something else for the patient who is very elderly. You need to cut a plywood board about 24" long by 8: wide to go over the two foot rests. This is not always needed, but it prevents the infirm patient's legs from slipping between the leg extensions. A stroke patient may not be able to tell you and you won't notice you are twisting and damaging their feet. I used to secure this when going out with a length of duct tape, and later with a belt of velcro.
Now you think about a velcro belt to keep the legs from slipping out. These are very inexpensive and locally available at the .99 cent stores for a buck. This should be very LOOSE, and simply prevent the patients legs from slipping forward over the edge of the plywood board or leg extensions.
Finally, you need to obtain some scotch-light reflective tape (comes in red, striped and yellow) to wrap around cylindrical surfaces. At night this tape will pick up a headlight and insure visibility. They have little blinking strobes, but the Scotchlight (available at auto accessory stores) will work as well and less trouble.
Of course you require an accessory bag to hook to the two handles that may be used for medicine, snacks, hydration (a small thermos), a blanket, cap, gloves, scarf, and most important a small flashlight. I prefer the fireman's disposable lights, but the new LEDS are super. I like to tape a cord to the flashlight and tie it to one of the straps on the accessory bag. Inventory this stuff before going out.