The difficultly of install is related to your desire & ability.
A few questions to ask yourself.
Do I have the basic tools for automobile work ( sockets, wrenches, torx drivers, screw drivers, etc ) ?
Do I have a soldering iron suitable for automotive electronics and can I solder?
Can I work in tight / confined places?
Do I have and can I operate a Digital Multi Meter? All wires should be checked & confirmed before install.
Do I have the time & money to buy supplies like cable ties in various lenghts, quality electric tape,
heat shrink tubing in various sizes, proper anti-mar trim tools for removing door and dash trim panels, etc?
Can I read and understand the install guides and wiring charts necessary?
The remote keyless entry part of the job will require removing the drivers door inner panel to access the lock module. That also means running the wires from the door back into the car. Sounds easy but to do it properly so it will last many years is the goal.
The remote start part of the job will require a bypass module to allow the car to start without the ignition key.
These modules must be attached to the car and the remote start unit and programmed to the car in accordance with their install guides.
Figure on about 6 hours of actual car time and almost that amount in procurement / research / prep time. Also be aware that units from DEI, Compustar and others come with a warranty "IF and only IF" they are installed by a dealer. Additionally, as a DIYer you will find it difficult to get any tech support from those companies.
Because of the door locks and the PassKey3 immobilizer, I would use the iDatlink ADS-DLSL GM1 bypass module with a quality remote start w/keyless entry system. This bypass module will control the doors, trunk, and car alarm with just one easily accessable wire connection to the car. Cost is about $50 and it would save a lot of time locating and connecting to the cars wires.
Here are a few links to get you started.
Bulldog Security for wiring charts and basic DIY remote start systems: http://www.bulldogsecurity.com/bdnew/vehiclewiringdiagrams.asp
AudioVox for wiring charts: http://techservices.audiovox.com/Login.aspx Membership is free.
DEI for bypass modules: http://www.xpresskit.com/VehicleCompatibility.aspx?p=-1&year=2003&make=Cadillac&model=CTS&ps=1&s=0
Fortin for bypass modules: https://ifar.ca/en/vehicles/cadillac/cts/2003/
ADS iDatalink for bypass modules: http://www.idatalink.com/helpdesk/
DEI Ready Remote DIY systems: http://www.designtech-intl.com/diy.asp
Good Luck!
Soldering is fun!