I would use whatever is already in there. But I say that with some reservations.
First, if you go to
http://electrical.hardwarestore.com/...onnectors.aspx, you will find pictures and names for a bunch of different types of low-voltage connectors. It helps to know the names when you are talking about them. I don't think you will need any rings, spades, or push-ins - concentrate on tap splices, butt splices, and wire nuts (aka twist-on) connectors. You will also note that connectors are kinda-sorta color-coded for the size wire they will handle.
I believe you will find that several of the connectors in your TM are "tap splices". These work nicely if you know how to use them (took me a while, and several wasted connectors, to figure it out). The clue is this - insert the wires,
open the gate flap, and squeeze the metal piece into place with a big pair of pliers.
Then close the gate flap with your fingers until it clicks.
The reason I have some reservations about this connector is that each one works with a small number of wires sizes, and TM seems pretty cavalier about violating that sizing. For example, yellow ones are intended to work with #10 and #12 wires, but in my 2002 TM, I found yellow connectors making a #18 tap from a #12 main line wire. They don't work well for a little wire and a big wire. So if you find that situation, go ahead and replicate it, but then tug on each wire to make sure it is solidly connected.
Butt splices? They work great in this situation if you have a crimp tool, but don't try to crimp them with ordinary pliers. Again, you shouldn't mix wildly different wire sizes.
Wire nuts? Also good in this situation, and unlike butt splices and tap splices, they work well when small wires are wrapped around a big wire - just use a connector that is right for the big wire size. Make sure they are tightly wrapped, and that none of the bare wire shows above the collar. After the conenction is made, many people wrap a few turns of electrical tape around the open end of the nut, but if it is tightly wrapped and none of the copper shows, I've not found this to be necessary.
Making a good connection isn't hard, just fiddly. Make sure to use a new connector in each case - don't try to reuse the old one. And finally, make sure there is some slack in each wire. The opening in the sheet metal has some sharp edges, and you don't want a wire stretched across such an edge. If a wire is too short, you can splice on a new piece as an extension, using either a butt splice or a wire nut.
Let us know how it works out.
Bill