There are two types of rectifier topologies that are interesting to DRSSTC use, half wave rectification and full wave rectification.
The following rectifier topologies are a trade off between cost to rectifiers, capacitors and what kind of performance you expect to get out of the Tesla coil. Look at chapter 4 about the DC link capacitors for more details about that component.
Diodes with isolated base plates should be mounted on the same heat sink for best possible thermal coupling, to ensure even current sharing. Stud mounted diodes should be installed in the same heat sink if they share the same potential.
To ensure a stable running DRSSTC that can put out consistent long sparks, it is important to have a constant DC supply voltage. If the voltage drops too much from supplying a large current, its called sagging. We do not want it to vary too much as spark growth will be limited by the falling DC bus voltage.
This is chapter 1: Rectifiers of the DRSSTC design guide
Examples of diodes installed as rectifiers in DRSSTCs
Single phase rectification
The following two waveforms illustrate the 1-phase half wave rectified and full wave rectified curves. The marked green area shows the amount of voltage sag between the mains 50/100 Hz cycle that the capacitor will have to act as a reservoir for. The larger green area, the more capacitance is required to uphold a certain voltage level and minimize voltage sag to predefined limits.
Three phase rectification
The following two waveforms illustrate the 3-phase half wave rectified and full wave rectified curves. The marked green area shows the amount of voltage sag between the three 120 degree phase shifted mains 50/100 Hz cycle that the capacitor will have to act as a reservoir for. The larger green area, the more capacitance is required to uphold a certain voltage level and minimize voltage sag to predefined limits.
To illustrate how much capacitance is needed to obtain certain voltage ripple / sag, take a look at the table in the graphic below. The numbers are linear against the current, so if you lower the current to 10 A (from 20 A in the illustration) then voltage ripple will be half of the table values.
I is Ampere, t is the conduction time intervals in seconds for 50 Hz (1 phase half wave 0.02, full wave 0.01, 3 phase half wave 0.0067 and full wave 0.0033) and C is capacitance in Farad.
The voltage ripple calculation and selected allowed voltage sag does not make it alone in choosing the filtering capacitance for the DC link. A larger capacitance could be needed depending on MMC / tank capacitor size, more on this topic in chapter 4: DC link capacitor and chapter 6: MMC / tank capacitor.
It is important that parallel rectifier diodes have the same lead length or busbar construction so that inductance and resistance in the layout is the same for all phase inputs. In the case of 4 parallel diodes supplied along a busbar, there can be up to 40% difference in the conducted current, those diodes mounted closest to the phase input will conduct the most current. 
It is not just electrical impedance that should be considered for parallel diodes. It should also be ensured that the thermal impedance and cooling is as close to even for all the paralleled diodes. This can be achieved by mounting the parallel diodes on the same heat sink and have enough margin space / heat sink mass so that one diode can not heat up one side of the heat sink.
Rectification conclusion: There are much larger benefits of full wave rectification, than saving a little on the cost for the extra diodes. The saved silicon also means that larger capacitors will need to be used, which will cost even more.
For 1-phase full wave rectification 6000 uF capacitance should be used to stay below 10% ripple at 20 Ampere, for 3-phase full wave rectification 2000 uF capacitance is enough to stay below 10% ripple voltage.
Despite insuring the best possible wiring and low inductance design around parallel diodes, it is still necessary to lower the current capability by 30-40%. This is to ensure headroom by account for differences in silicon, temperature and circuit layout.
In some countries where mains power is only 1-phase in most house installations and ranging from 110 to 200 VAC, it can be necessary to use a voltage doubler to get a sufficient high voltage in a easy and cheap manner.
This is a full wave voltage doubler, it consists of two half wave rectifiers in series charging each their capacitor. The resulting voltage across the two capacitors is a doubled voltage of the input.
A simplified half bridge DRSSTC inverter is also shown with the voltage doubler incorporated.
Installing a voltage doubler with two capacitors directly on top of the IGBT switches is not always easy or even possible. An extra capacitor that can withstand the full voltage of the voltage doubler can be used to mount directly on the IGBT switches.
 Jean-Luc Schanen, Jean-Michel Guichon, James Roudet, Cyril Domenech, Luc Meysenc. Impact of the Physical Layout of High-Current Rectifiers on Current Division and Magnetic Field Using PEEC Method. IEEE Transactions on Industry Applications, Institute of Electrical and Electronics Engineers (IEEE), 2010, 46 (2), pp892-900.