As Gonbechan says you shouldn't have much difficulty registering as a farmer if your father in law is onside and you may even count as one as you are part of his family. I'd chat with him before going to speak to your local council, family connections are everything. Many folk will probably just assume you are a farmer because of your connection to his family and your wife may already count as a farmer so you by extension of being married to her may also count. As to your question about your local council worrying that you are gaijin, that shouldn't concern them overly. One other thing, if you are renting a small plot to grow food for yourself, although technically you should be a farmer the reality is that no one is ever going to check or even ever likely to enforce that requirement and one of the routes to becoming a farmer is renting a plot of 1500 tsubo and growing on it.
Having a connection like that will help you immensely, he can probably help you find a spot of land to start growing on (once word spreads that you are looking for a plot of land all sorts of plots start turning up that are not being used) and can also help you get a poly tunnel from someone that is no longer using it. We have four vinyl houses that have all been given to us by people who didn't want them anymore. If you want to grow sweet peppers and tomatoes then you will need one, growing tomatoes outside can be hit and miss depending on the weather and peppers do much better inside where you can control insects and disease much easier.
Your father in law can also probably help you get some basic equipment like a rototiller from someone that is no longer using theirs or has bought a newer one. We've been given several by friends of my wife's parents, so if you let it be known you are looking for one word will spread through the grapevine.
Try not to get involved with JA if you can help it as that will restrict your options later on, just maintain a friendly distance without committing yourself if they make an approach. If you do get involved quite often they will expect you to buy all your inputs from them and then expect you to sell all your produce through them at the price they set, which is not favourable to you. You can do much better opening your own sales routes.
Some further reading for you
- My favourite writer on market gardening. The New Organic Grower should be your bible, loaded with practical advice and tips and an all round invaluble guide to market gardening.
- His book is highly recommended, lots of useful information, tips and techniques and his style doesn't involve lots of mechanisation so no high outlay to get started.
- If no dig growing is your thing then Charles Dowding should be in your library. As with the other guys his books are an awesome guide to someone starting in Market gardening.
- His Youtube channel is fantastic, lots of free and practical advice for a new market gardener. Not everything he says is applicable to Japan and sometimes he does make mistakes (which he is honest about) but you can learn from that so you can avoid them.
All of those guys are market gardeners and you may not choose to go down that route. A friend of mine sells around 20 million yen a year of broccoli, cauliflower and nasu using just two rototillers (one for mulch laying and one to build up raised beds) and he reckons market gardening is too much work and too complicated and after seeing his farm I agree he does have a valid point but I like market gardening.