As to the software, that’s easy. Do it the right way and learn illustrator, or even affinity. Inkscape doesn’t even export to CMYK – a first-hurdle fall if you are looking at print. You need to understand these sorts of things before even thinking about starting a print-based business.
Free always comes at a cost.
However, the software question is possibly academic, because, reading between the lines, I’m guessing you are not a designer and have little or no experience in this area? Yet, you talk about jumping into a highly-competitive area where a lot of qualified designers will be your competition. Granted, there is an awful lot of rubbish out there too from stay-at-home mums who were good at art in school. It is still a very busy place to be and you’ll have to bring something new to the party.
If I am wrong and you are an experienced designer or have fashion industry experience, I apologise, but the question leads me to think not. The fact you want to start a business looking at free tools, straight away rings alarm bells.
I am by no means saying don’t do it, but go in with your eyes open. You even say you are a beginner, which, in itself is fine, but a beginner is a long way from starting a business you expect to bring an income.
‘I want to open a car repair garage, what kind of spanner do I need?’ See what I mean?
Of course, I know nothing about you, your business plan, or your ideas, but simply based on your initial question, I’d say you are wanting to run before you can walk. Had your question been, ‘what is the best vector illustration software?’ Of course, I’d still refer you to my first para.
So to that end, why t-shirts? I get it, I’ve been looking at a side shizzle for ages. One day, I’ll find the time! But what are you looking at that is going to make them desirable? Are you a traditional illustrator and want to get into digital? Do you have a specific idea that you think is unique and has legs, or is it simply, that’s a good Etsy business you can do from home and have the time to be there for your kids? Spoiler; start any business and make a go of it, you are very likely to have less free time – at least in the first couple of years. A business like that will be all about brand and marketing if it has any chance of standing out from the crowd. Is that your area of expertise?
Well, you did say that you wanted different perspectives. Careful what you wish for!
I am not saying this to be negative, but just exploring the alarm bells that rang when I read your post.