Where do you get your fabrics?
Lots of places! So let me break it down for you:

PLUSH FABRICS:
United States Resources:

◾ JoAnn Fabrics: JoAnn’s is a good beginner resource for fleece and some minky. They often have sales and coupons and offer free shipping for larger orders.

• Anti-pill and Blizzard brand fleece work really well if you want a cheap fabric alternative for beginners (just be sure to catch it when it’s on sale — it’s almost always on sale).
  
  They’re continually coming out with more plush fabric options, though the colors can be limited:
• Solid minky is not quite as stretchy or thick as better brands, but will still work decently.
• Dimple dot minky comes in a lot more colors, but has a dotted texture. Great for babies, but it might not be what you prefer.
• Sew Lush is a double-sided kind of thick plush minky.
• Sherpa fleece is very thick and stretchy. Often used for jackets and outerwear, it works well for big pillow-sized plush.
• Pure plush fleece is another double-sided minky with 2-way stretch. That means it stretches both widthwise and lengthwise. This kind works well for plush that are extra squishy (like a Squishmallow plush)
• Swirl faux fur is a slightly longer minky with a rosette pattern in the fur.

◾ Howl Fabrics is an independent brand offering minky and faux fur. They don’t have a free shipping option, but their selection is very extensive.

• Minky cuddle solid is their selection of Shannon brand minky. This is often considered one of the better brands of minky. They have nearly every color in the Shannon catalog as well as their own colors (labeled “HF” in the name). They offer smaller quantities of swatches, fat quarters, half yards so you don’t have to commit to a lot.
• Teddy & bunny fur is their vast array of medium-pile (about 1″ long) faux fur. It does not stretch so it’s more suited to costumes and fur suits. But it could also be used for classic teddy bear style plush.
• Luxury shag fur is their vast array of long-pile (about 1½” long) faux fur. It does not stretch so it’s more suited to costumes and fur suits. But it could also be used for larger plush or doll hair.

◾ Cali Quilt Co. has both an independent site and a shop on Etsy. They carry many colors of smooth minky and luxe cuddle. They offer free shipping with larger orders.

• Smooth minky has nearly all of the colors from the Shannon catalog. There’s a lot to choose from, so it might help to pick a color from the Shannon catalog and search for that name. They offer smaller cuts like fat quarters and half yards so you don’t have to commit to much.
• Plush minky shows the luxe cuddle collection from Shannon. These have a longer pile (usually 10mm or so). There’s a lot to choose from, so it might help to pick a color from the Shannon catalog and search for that name. They offer smaller cuts like fat quarters and half yards so you don’t have to commit to much.

◾ Missouri Quilt Co. is a quilt shop that offers a nice selection of smooth minky and luxe cuddle.

• Cuddle solids shows their selection of mostly Shannon brand solid smooth minky.
• Luxe cuddle shows their selection of Luxe Cuddle Shannon fabrics.

◾ Big Z Fabrics offers a selection of their own brand of minky at lower prices. They’re slightly lower quality than Shannon and offer fewer colors, but they’re still a solid option. Big Z is unique because they offer their own version of mochi minky, which is a thinner 4-way stretch minky popular for extra-squishy plush like Squishmallows. They also have fleece and a wide variety of faux fur.

◾ Fabric Empire offers a selection of fleece and minky at lower prices. These are their own brand, so they’re slightly lower quality and fewer colors to choose, but still a solid option.

◾ Spoonflower: This service offers custom-printed fabric. I use it to make custom designs for minky, fleece, and cotton.
You can create your own design or choose your own from their marketplace of designs submitted by others. The price can be a little high compared to solid fabric, but they do sometimes have sales and coupons to help soften the blow. The main issue with the fabric (and many custom-printed fabrics) is that the ink from the printer does not penetrate through the entirety of the fur. So the base of the fur still shows up white — especially in dark fabrics. One workaround is to use lighter colors, but also to opt for textural designs, especially ones with flecks of light colors. For example galaxy prints help you get away with the drawbacks of the fabric.

International Resources:
I haven’t personally shopped with any of these international sellers, but I’ve heard good things from other sewists. So these weren’t found based on a simple Google search. Please do let me know if you have any others to recommend!

Canada – Funky Monkey Fabrics

UK/Europe – Rooftop Fabrics

Germany/Europe – Stoffhummel

Australia – Minky n More

What sewing machine do you use? Any recommendations?
I currently use a Husqvarna Viking Emerald 116. I’ve had it for over 20 years now and it still works very well despite what I put it through! It’s a mechanical machine that only does the basics, but it does them very well. I also have a Heavy Duty Singer machine that I use as a backup.
I personally got the Singer so I could test it as a good beginner machine, it has worked out well for me so I would definitely recommend it to others.
But if you’re able to do a more thorough search and go to a dealer to try different machines, you’ll have something that will be better suited to exactly what you need.

What embroidery machine do you use? Any recommendations?
I currently use a Husqvarna Viking Topaz 50 for my embroidery machine. I’ve had it for over 6 years now and has heartily put up with everything I do to it, haha! As far as price, it’s a bit in the mid to high-range and ran me about $2000 refurbished. So I would not recommend it for someone just starting out and wants to spend less.
I have also used a Singer Futura in the past, which had a good handful of problems. It didn’t completely prevent me from embroidering, but I don’t believe it’s a brand I would return to.
For a beginner, the Brother brand has been gaining traction as a reliable budget brand. I personally have a mid-range Brother Innovis NQ1600E I use as a backup. But beginner models like the SE600 or SE1900 get good reviews in general and from other embroiderers. Ideally, you should purchase a machine that has an embroidery hoop suited to the projects you’ll be making. In the case of plush toys, the minimum 4″ x 4″ will still work, but may limit you with many designs. A 5″ x 7″ hoop will give you much more freedom by comparison.

What embroidery software do you use? Any recommendations?
I currently use a program called Hatch by Wilcom. It’s in the mid to upper range as far as price, so it has a few more robust features as well as fewer bugs. Keep in mind, this is a digitizing program, so it allows you to create entirely new embroidery designs from scratch. Programs that just have editing capabilities (such as resizing, rotating, etc.) are much less expensive and often come for free with your embroidery machine.
As far as digitizing programs for beginners, I would recommend a program like Embird or Stitch Era Universal. Both of these offer free trials so you can get a feel for the program before you buy.
As for simple editing programs, there is a free program I have personally tried for testing purposes, called MyEditor. This program will allow you to make simple edits to existing embroidery, including combining files (really helpful if you want to build custom faces from separate eyes, noses, mouths, etc.).