Step 1: Calculate Design Parameters

Everything starts with the standard thrust equation:

A holistic approach would be to consider your fuel and oxidizer choices and what the kind of performance the mixture will give you at your chosen chamber pressure then run through all of these equations:

However, I have been through this rodeo before so I took a shortcut and used NASA's CEA software which is much faster, but you need to have at least gone through the process of deriving all of the equations by hand before you can really understand and utilize the software.

CEA output for the IPA/N2O mixutre at 20 bar (300psi) chamber pressure: 

		CHAMBER	THROAT	EXIT
Pinf/P		1	1.7344	18.987
P,	BAR	20.265	11.684	1.0673
T,	K	3353.31	3173.12	1962.93
RHO,	KG/CU	1.8931	1.1686	1.73E-01
H,	KJ/KG	1820.97	1251.23	-652.7
U,	KJ/KG	750.52	251.43	-1271.19
G,	KJ/KG	-32276.2	-31013.7	-20612.2
S,	KJ/(KG)(K)	10.1682	10.1682	10.1682
M,	(1/n)	26.046	26.388	26.388
Cp,	KJ/(KG)(K)	4.7167	4.6253	1.5256
GAMMAs	1.1435	1.1397	1.2592	1.2613
SON	VEL,M/SEC	1106.4	1067.5	882.9
MACH	NUMBER	0	1	2.519
PERFORMANCE	PARAMETERS
Ae/At		1	3.25
CSTAR,	M/SEC	1624.5	1624.5
CF		0.6571	1.3692
Ivac,	M/SEC	2004.1	2502.3
Isp,	M/SEC	1067.5	2224.3
MASS	FRACTIONS
*CO	0.1046	*CO2	0.14206	*H	0.00046
HO2	0.00003	*H2	0.00191	H2O	0.11395
*NO	0.01804	NO2	0.00002	*N2	0.5644
*O	0.00535	*OH	0.02117	*O2	0.02799

From which, I had all of the other inputs needed to derive:

Calculated Design Parameters
	Injector	Fuel	Oxidizer(x4)
	Flow Rate:	12.24	75.74	gallons/hr
	Pressure:	349.86	735	psi
	Injector Diameter:	0.0368	0.0300	inches
	Chamber
	Injector	Throat	Exit
Pressure	298	172	16	[psi]
Temperature	5577	5252	3074	[F]
Density	0.118	0.073	0.011	[lb/ft^3]
Speed of Sound	2475	2388	1975	[mph]
Mach Number	0	1	3
Local Velocity	0	2388	4975	[mph]
Cross Sectional Area	1.52	0.13	0.41	in^2
L* chosen for propellants	50	inches
Length of the chamber	3.937	inches
Chamber Convergence Angle	60	degrees
Rocket Nozzle Divergence Angle	15	degrees
Wall Thickness	1/16	inches
Temperature Change Through Wall	18.8	F
	Coolant
Maximum Wall Temperature	125	F
Coolant Flow Needed	129.5792673	gph
Coolant Velocity	30	ft/s
Gap needed	0.01	inches

Now that I have all my numbers, onto the design phase!