-What do you suggest as a good strategy when lighting outdoors? Or would you say to just go ahead and invest in a cheap lighting kit?
-If so, what lighting kit would you suggest? I was looking into the redheads 3 piece kit online.
Redheads are tungsten balanced, so won't match colour wise with the daylight. You'll find it tough to power them and you'll struggle to get enough power out of them to combat the sun, assuming a bright sunny day. A cheap lighting kit just isn't going to cut it. If you can rent HMIs, that's a different story.
But, you've got the most powerful light available for free - the sun. Your best bet is using the sun to your advantage and shaping the light to what you want. I can't tell you how to light your scene, as it is your scene, your lighting scheme, your ideas, and you know what mood you want to create and what look you want.
I would suggest, however, using a combination of the following:
-Reflectors - generally a lot harder (but stronger) bounce than something like:
-Poly Boards or Foamcore - generally a softer light bounce. This is my go to bounce source.
-Diffusion gels/diffusion frames - I have some wood frames with 216 in them. Good with a cardellini or matthelini clamp for use on C-stands if you want to soften a smaller area of the light.
-Silks. These come in a bunch of different sizes. You can use smaller ones to just cover certain areas of the frame, cover your whole frame (depending on your frame size) or you can use larger ones to cover your whole frame. What is also common is placing a large silk above your scene to soften the sunlight.
-Floppies and/or large flags. These are good on C-stands to cut light off certain areas - they cut a whole lot more light than the silks which mostly softens (as well as cuts) the light.
-Black Duvetyne and Muslin (perhaps Bleached Muslin) - black and white material that prove really good for bouncing or cutting light where you need. Keeping rolls of this stuff around means it's really verstatile - you can cover a large or small area really quickly.
The most expensive things here are silks and floppies. Also, depending on the look you want and the camera you're using do tests at different times of day and make sure you schedule so you're in the right place at the right time for the sun