Congratulations on your new machine! I also have a Janome 6600P and 350e...and love them.
I will try to answer some of your questions, although I certainly am not a professional–so take my advice with a grain of salt.
1. Needles - I got Organ needles (recommended by my Janome dealer) from allbrands.com (100 needles for $29.99) -http://www.allbrands.com/categories/852/2039-organ-japan-15x1st-hax1st-box-100-home-embroidery (I use Schmetz on the 6600P–I got 100 from Jhittle for under $30).
2. Stabilizer - I bought generic stabilizers from ebay. I use tear-away for cottons; wash-away for free-standing lace or thinner material. I haven’t found the need to buy different stabilizers for each fabric–you can always use two pieces of stabilizer if you think thicker is needed for an intricate design. (Using cheap stabilizers creates more “dust” in the machine, so I thoroughly clean the machine frequently.)
3. My dealer strongly recommended Madeira polyneon...not rayon (she sells all brands, so I followed her recommendation). I have never had the first problem with the thread. I buy my thread from
http://www.thesewphisticatedstitcher.com/ - their prices are the best and the service is wonderful (they also sell needles and other supplies).
4. I order bobbin thread from The Sewphisticated Stitcher - Madeira 10,936 yard cone of bobbin thread for $15.00 (it lasts a very long time).
5. Your trial definitely indicates a need for adjusting the tension. It appears that the top tension is too tight. Try loosening it and see if it looks better.
Embroidery sites - Embroidery Library is my favorite site, by far. Their designs are wonderful. I also like designsbysick.com - they have some really cute designs. You can pay a $15.00 membership fee that is good for one year and allows you to download all of their designs. I did that when I first got my embroidery machine. Then, they ran a special where I paid less than $100 and have a lifetime membership, plus they sent all the designs to me on a CD. I have gotten my money’s worth from that site.