N.B. 'soundfield' here means the type of microphone, not necessarily the manufacturer called 'SoundField'
My main microphone is the TetraMic from Core Sound. This was the first 'affordable' soundfield microphone, and the first to use software instead of hardware for calibration and to generate B-format. Sometimes I use an SPS200 from SoundField. This has larger capsules, which makes it quieter, but the larger spacing means that the imaging at very high frequencies is less accurate. I have had this microphone independently calibrated by Core Sound, so that it matches the TetraMic in tonal quality and can be processed using the same software. Although they each have four capsules, both of these microphones use a single cable to the recording equipment, and so can be used moderately discretely.
My first commercial recordings were made using a pair of AKG C414B-ULS microphones which are still part of my kit. The C414 line is the solid-state successor to the classic C12 and C24 valve microphones. Also from AKG I have a number of Blue Line microphone bodies and a range of different capsules. These were originally acquired in order to assemble a 'Native B-format' array for ambisonics.
Recorders and interfaces
Typically I record using a Tascam DR-680MkII portable recorder. This is a good quality device which can record four channels at once with matched gains, as is required for use with soundfield microphones. On occasion I record directly into a laptop computer using a MOTU 8pre interface which has eight inputs and so can record two soundfield microphones simultaneously.
The Zoom H2n is a very convenient recorder for location work, or for backup recording. It can even record surround directly to an Ambisonic B-format file, though without a vertical signal. There are four microphone capsules built in to it (but not in a tetrahedral arrangement).
Many of my early amateur recordings were made using ribbon microphones made by Reslosound; I first acquired second-hand a pair of RB/T microphones from the early 1960s, and later a new pair of the restyled MR.1 from the later 1970s. More recently I used a Sony electret microphone sold for use with video cameras: the ECM-959V. I still also have a Sony WM-D6C 'Pro Walkman' that I used for many years with the iconic ECM-929LT, which together made a superb highly portable recording package.