Enlarger -- it depends...the last time I was in Japan the enlargers I saw were quite expensive, but maybe you could get a used one fairly cheaply. I would recommend getting something that could do MF, but if there's a big price difference there's no harm in starting with something smaller. Make sure it comes with enlarging lenses as well.
Trays -- this may depend on how many sizes you print, and how many processes you do. I've got trays (at least 3 in each size) that runs from 4x5 to 11x14. I prefer to use trays that are one size larger than the print I am using. You may prefer to use tongs as well, to get the prints in and out of the chemicals (gloves could work too, but you'd have to be careful of cross-contamination).
Clips -- go to the 100-yen store and buy some cheap plastic clothes pins -- they work great for film and prints. Of course, you'll need something to hang them on -- for film I use those little square hangers that have many (8-16) clothes pins on them (usually used for hanging underwear or small things), for prints I bought a laundry drying rack (for sweaters and things) and hang the print off that using normal clothespins. I've tried lots of different clothes pins (!) but the best ones were from the 100-yen store. For fiber paper I prefer to lay the paper flat on screens, but that may be difficult to store considering the storage space limitations in many Japanese apartments.
Blackout curtain -- I guess this will depend on where you are living and how many things you need to black out. When I was living in a house I blacked out the windows with two thick garbage bags and painters tape -- it wasn't pretty, but it worked, as I had three windows and a door to cover up. Now I I use a blackout curtain for one door -- went to the fabric store and bought the cheapest fabric I could find -- it's hot pink (!), but it works great.
The easel help keeps the paper flat (a lot of paper, especially fiber, has a curl to it when taken out of the package). I recently have been using Fujibro paper (RC) and that stays nice and flat -- I really didn't need an easel for it, except that I wanted white borders for my images. I suppose you could tape the paper flat to the baseboard, or use really clean glass over the paper as well...I'm sure others will have different suggestions.
You will probably also want dedicated graduates for measuring out chemicals and liquids -- again, the 100-yen store is your friend. I was only in Japan for a couple of months last summer so didn't want to buy a lot of stuff, but I was able to get by for film developing with a little ingenuity. I also noticed that at Yodobashi Camera and Bic that a lot of the darkroom stuff was actually cheaper than what it was labelled on the shelf. I got a 20000 yen camera backpack (discontinued) at 3000 yen (but the price on the shelf was 8000). A large graduate -- labelled 3000 yen, I got for less than 1000 yen. Maybe I was just lucky -- I don't know where you are located, but that's something to consider as well.