No 1: NOTHING is ESSENTIAL. There are always alternatives.
I prefer to use propagating mix to strike cuttings
http://retail.debco.com.au/products/spe ... gation-mix. Most nursery outlets will have this or a similar product. It is fairly sterile so less fungal/bacterial infection on the fresh cuts, holds water but also drains well so good air too which are all essential for success with cuttings. I have not used the peat pellets but they might work.
I also prefer slightly larger pots to maintain moisture around the cuttings. 75mm full depth plastic pots work best for me. That might mean the mini propagator is just a little too shallow for pots and cuttings.
Humidity is essential. Automatic misting is the ultimate for striking cuttings but below that any closed container will suffice for many species. That's what the mini propagator will do for you - maintain high humidity. Some alternatives I have used successfully: Plastic bags over the pots can work ok; For larger numbers, Clear plastic storage tubs with lid
http://www.bunnings.com.au/award-50l-pa ... s_p2580445- Place a couple of bricks in the bottom, fill halfway up the bricks with water to maintain humidity then place your pots of cuttings on the bricks (or boards/mesh/etc sitting on the bricks). Keep the lid on until cuttings show signs of growing then you can leave it propped open slightly to start hardening the growth.
Rooting compound is a definite advantage in getting harder to strike species growing. I know that some growers use honey and/or vegemite but my tests show that rooting gel has definite advantage and gel is superior to powder for me.
http://www.bunnings.com.au/propagation- ... 0_p3012537
My first ever attempt at striking White pine had 100% success (1 plant from 1 cutting

) but attempts since then have been less successful

. It is possible to strike white pine cuttings but you are starting with the more difficult species so be prepared for less than spectacular results.