I do like Ivah - and I don't see it as a lot of work, but maybe I'm missing something - or under-estimating " a lot of work"?
I grow everything (pretty much) in pots, then plant out.
I don't need a lot of each batch - 3 or 4 lettuces twice a month is plenty, ditto for Cauliflowers and so on.
I sow a few seeds twice a month, using 1/4 size seed trays, usually with 3 varieties per tray. I reuse the little trays / seed sowing compost all season, just soak them, let them drain, and then sow some more. Reusing the same trays for the same seeds would mean that any late germinating seeds were for the veg you were expecting! I have a list of things that germinate at the same speed because it is hard to prick out if one part of the tray isn't ready ...
I prick-out into pots when seedlings big enough, and plant out when plants are big enough. Its probably about 20 - 40 plants in each batch (allowing for some things like Sweet corn and beans where more are required).
Some things I put more than one per pot. Beans get 2-per-pot (rather than using smaller modules and putting two plants per cane
) and beetroot get 3 per pot, around the edge, and two are pulled "young" to allow the third to mature. Ditto carrots (but I sow them direct into Richy's Paper Pots along with anything else that doesn't like being transplanted
I have pot-holders that hold 20 x 3" / 3.5" pots. Makes the whole thing easy being able to pick up 20 plantlets at a time
You do need a bit of some space though,a nd a greenhouse / conservatory.
I get nice sturdy plants when I plant them out - rather than sowing direct where the little seedlings are munched by bugs before they get big enough to have some ability to survive. We have heavy clay soil, so growing plants helps as seed drills are very hit & miss. Plus I only have a few of each type of plant. A long row of cauliflowers is no used to me, they'll all be overblown inside a fortnight (I could freeze them, but we grow mostly for in-season-dining, and freezing requires quite a lot of work).
I grow in 3" pots for things that will be potted on (Tomato / Cucumber etc. that don't get planted out until they are in 6" or large pots) and 3.5" pots for anything going straight into the ground. That gives me a little bit more leeway in case I'm busy when they are ready to plant out, or the weather is bad. With 3" pots I find once they have got to planting out size the plant quickly starts drying out, needing feeding, struggling ...
But do please tell me if you think I'm mad!