If you want to make great recordings that are easy to edit afterwords you will likely want to invest in a good computer if you don't already have one.
check out this page for more info on picking out a computer for recording.
I would highly recommend using a computer as your recording device. If you already have a computer you may be able to use it for recording. There are alternatives though if you don't have a computer that works and are unable to afford one.
If you have a phone there are apps that you can use to record with. These can work alright but I would recommend investing in an external microphone because the built in microphones are not great for most recording situations.
There are also good portable recording devices. Check out this page for more info on Audio Recording Devices that may work for you.
Once you have a recording device setup and ready to go the next thing you will need is a way to capture the audio sources you are wanting to record. This will require a microphone. Check out this page for more info on microphones and the best types for different recording situations.
If you are using a computer or phone as your recording devices you will also need an audio interface to convert the signal coming from your microphones into a digital signal that your computer can use to record. check out this page for more info on Audio Interfaces
Next you will need software for capturing and editing your audio. On a computer these are known as DAWs or “Digital Audio Workstations”. Check out this page for more info on different DAWs and which ones I recommend.
Along with a DAW you may want to invest in some good plug-ins to help you get that sound you are looking for. Check out this page for more information on different Audio Software I’d recommend.
After you have these main components setup you will be ready to do some basic recordings. Next you will likely want to invest in some accessories for your studio. These are things like mic stands, head phones, cables, Di boxes, Midi controllers etc. What types of accessories you will need will depend on what you are wanting to record. Check out this page for more information on different Audio Accessories you may want to invest in.
In order to record or stream video you will need some kind of camera to do it. The good news is most phones and laptops now a days will have a camera built into the device. These will be OK in some situations but you will likely want to invest in an external camera for capturing your video. Click here for more information on different types of Cameras.
If you are wanting to stream the video captured from your camera or if you want to capture videos from your camera directly to your computer. You will want to invest in a video capture card. Click here for more information on Video Capture Cards
After you have the video files on your computer you will need a way to edit it. That where video editing software comes into play. Click here for more info on Video Editing Software.
A camera is a device that captures light. If the location you are trying to film at doesn't have good lighting you will need to provide extra lights if you want a good image. Click here for more info on Lights.
You will also need some accessories for your camera depending on what you are wanting to film. This could include tripods, green screens, lens etc. Click here for more info on Video Accessories.