Tabi are not actually "martial arts foot wear". They are in fact a type of sock that the people of Japan use to wear. They would fasen in the back with kohaze, and only come up to the ankle. If you want shoes for training I would recommend getting what is typically called "wrestling shoes". they are designed for use on the mat, and though they are made for ground work, they work fine for strikers as well.
These days it's fairly common in most schools to be barefoot. However I know a lot of schools don't allow this anymore do to hygiene reasons. I would also ask where you are training? Are you on a mat? In the woods? At home? Park? etc. What you wear on your feet and the system you are studying should weigh on your decision.
Skeletoes are very popular to wear for training, my sifu loves them and so does a few others in my class.
As far as "ninjutsu tabi" there is no such thing. If your talking about those high boots with the soft rubber soles, those are called Jika Tabi. (jika meaning it contacts the ground, as tabi do not. you wear tabi in doors or outdoors with wood or straw sandals). Jikatabi are a combination of kyahan, tabi, and geta. They are not "ninjutsu tabi" (though I've seen alot of practitioners wear them), they are a modern adaptation that is popular for many people in Japan today. Farmers, construction workers, or even regular people love them because of how comfortable they are. They come in many different patterns and wearing styles, some have floral patterns inside so you can fold the tops down. They make ones lined with rubber around the foot to protect against water when farming.
Most are cloth, with just a thin rubber sole. It's like wearing a slipper. If you want a pair of these I would look into the rikio fighters (imported from japan). Just make sure you measure them right, they should fit like a glove. If not your feet will slide around on the inside. Especially if your on a mat, the bottoms will grip but your feet will move a bit. These are hard on your feet when on hard ground as it's very close to being barefoot, but can be very comfortable as general foot wear. I own a pair but because my calf muscle is 28" around at the top, I could only fasen the normal rikio fights up just past half way hahaha. I had to get the shimebuto version which adds girth to the top of the boot. If your training I would also get socks for the inside so you can wash the socks after training. though jika tabi breath fairly well, if your training right your gonna sweat
As far as gloves it depends what you'll be doing. They make all sorts of gloves, bag gloves, boxing gloves, fingered gloves, mitten gloves. Will you be doing full contact? will you have other gear on (ie helmet and chest plate). will you be doing "tag sparring" etc. Your instructor will be able to answer a lot of these questions. However I would get on century.com they have a wide range of sparring gloves. I don't like to wear gear, (which I DO NOT RECOMMEND). however if I was going to wear gear, I would want something that lets me open my hands because of the systems I study.
I was browsing the forums, just seeing what is out there, and not much was said in response here I didnt' even look at the date...
So even if the original poster doesn't see it, maybe someone who has the same question and sees this post can at least consider some of the things I've said
:EDIT: actually most of the posts are very very old :S I figured the top is the most recent