Hey Eve, I am a big fan of digitally generated patterns. You can save em to a cloud or hard drive, email across the world, rework or rescale them easily. You can even post them online for feedback as animated gifs and see an estimate for transformers and glass needs on design too. When your done with the pattern it doesn't have to live on a shelf forever- throw it on the floor to catch paint drips, or recycle/ burn it, whatever. When you need it again- you can always plot off another.
I used to use Adobe Illustrator, which works well and is a super capable design program. Adobe however is a profit (and data) hungry goliath, and most neon benders wont use most of illustrators capabilities and could probably use the extra $20 or so a month that illustrator costs for something else.
I switched over to inkscape about a year ago and have been loving it. Free, open source and very fully featured, it can do everything I need illustrator to do an more, and usually in a quicker, more direct way. It would be good to throw the developers a few dollars here an there- it isnt always as polished as illustrator in every aspect. Good to double check its scaling on some exports- not usually a problem, but it could be an expensive issue if you dont see it. Ethically, I believe in the open source communuity behind the program- its neat to think that anyone can add custom features and add ons to the software and that it is built to be user customizeable to their needs.
Whichever you choose, I recommend playing the bezier game to get aquainted with the pen tool, and learning the hotkeys for the program you use- they make it feel like a more natural tool. Staples or a local copy shop offer architectural blueprint printing services cheaply, but a vinyl cutter (the wider the better), big roll of paper, and refillable ink marker are invaluable tools with this process. There are a number of online tutorials for both of these programs to get you started. Stephanie Lifshutz even made a pattern making illustrator video. I find myself looking up how to do specific things in inkscape on occasion- the answer is usually just a few clicks away.
Happy editing :)