The localizer approach used to be the best "dive and drive" you could find because of the accuracy of the localizer beam. Now you are better off with an LPV approach. You should fly your localizer-only approach with a Continuous Descent Final Approach Descent techniques if you can. Refer to ILS for background information about:
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
If you have ASC 007 you are a Category C airplane unless you have a maintenance logbook entry raising your maximum landing weight. If you do not have ASC 007, you are a Category D airplane, end of discussion. See G450 Procedures & Techniques / Approach Category for an explanation.
Photo: MCDU arrival page (CYHZ), from Eddie's aircraft.
Approach selection is made either through the MCDU (NAV > ARRIVAL) or the NAV display.
Photo: DU arrival page (CYHZ), from Eddie's aircraft.
There is an advantage to making this selection on the NAV display: if the appropriate chart is selected in green from the CHARTS page, future changes to the approach on the NAV display will automatically change the selected chart.
[G450 Aircraft Operating Manual §2B-05-50 2.A. (2)]
Alternatively, you can preset the localizer frequency and the approach back course. (This would be advisable if you expect to be on a complicated STAR with short vectors to ILS final, precluding the auto-tune function.) You would enter the ILS identifier into appropriate LSK in the PROGRESS page and the ILS approach course in the Display Controller PREVIEW submenu.
Figure: LNAV Mode Selection, from G450 Aircraft Operating Manual, §2B-08-00, Pg. 7.
The book isn't very clear about this, but it is a basic function we've been doing for as long as we've had flight directors: use LNAV only for localizer only, APPR for an ILS.
Figure: Loc Mode Arm, from G450 Aircraft Operating Manual §2B-08-00, Figure 26.
[G450 OM 2B-08-120 ¶17.] The LOC mode automatically intercepts, captures, and tracks a front course localizer beam using the selected navigation source displayed on the coupled PFD. The LOC navigation source is selected using the display controller. The aircraft flies the heading intercept and is armed for automatic LOC beam capture.
Figure: Localizer Mode, from G450 Aircraft Flight Manual §2B-08-00, figure 25.
Be careful about the intercept angle. If you are in LRN mode the FMS should do a fine job of leading the turn if your speed is fairly constant. If you are in SRN mode with a large intercept angle, the FMS doesn't seem to grasp the distance to course until it is too late.
Figure: Localizer Course Tracking, from G450 Aircraft Operating Manual §2B-08-00, Figure 28.
[G450 OM 2B-08-120 ¶19.] The track submode, shown in [the figure], is annunciated the same way as LOC capture mode. There is no annunciator change that occurs at the capture to track mode transition. The track mode follows the capture mode and occurs after the beam deviation is reduced to a minimal value. In the track mode, the flight guidance computer automatically compensates for crosswinds of up to 45_ of course error.
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Gulfstream G450 Aircraft Service Change 007C, Maximum Landing Gross Weight, 58,500 pounds, Category C, Provisions, October 26, 2011