To provide a context, the following are my observations and opinions and are as a result of 22 years at Philmont, hiking most of the trails. This includes one year on staff as manger of logistics.
Cathedral Rock: Short hike to a fairly good camp nestled below the Cathedral Rock reservoir dam.
Lambert's Mine: From Cathedral Rock you will take a trail out of the creek gully up and around the reservoir. Then follow up the valley, going north to the Hunting Lodge site. A side road branches off the main road below the lodge. This side road only goes a short distance (100 yards or so) and peters out at the creek. Across the creek the trail leads up the valley to Lamberts Mine. This is an easy and pretty hike but your packs will be heavy with a full load of food. There is no mine at Lamberts, only a small camp in the valley floor, heavily wooded. After setting camp, take the old mine road around the ridge to Cyphers Mine. Easy and short side hike, good program. Tour the mine and maybe take a shower.
Mt. Phillips: Hope you have eaten your heaviest meals. This is a tough and long climb and you haven't yet fully gotten used to the elevation. Go back to Cyphers Mine and take the trail above the staff cabin up to Thunder Ridge. Be sure you have lots of water, Cyphers will be the last practical water source you will find until tomorrow at Clear Creek. This is a new trail and not terribly steep but quite long. It wanders all over the place until it breaks out onto the road at Thunder Ridge. Across the road is the new trail that goes up Comanche Peak. Just below the peak you will leave the new trail and scramble up a short distance on the old, rocky trail to Comanche Camp. This is a dry camp near the top of the peak. Just beyond is the actual summit. You can't see anything from the top as it is fully covered with trees. Drop down into the saddle between Comanche and Phillips then climb Phillips. This is a fairly tough trail but not a long climb. Phillips has a long top. You will break out on the rocky bare eastern end then return to scrubby trees on your way to the true summit on the western side. The campsites are just to your right immediately before the true summit. They aren't very good, rocky and not level and there is no water up there. The view from the summit is great and watch for the sun setting to the west. The snow-capped peaks to the west are Wheeler Peak, highest mts. in New Mexico.
Porcupine: This is a downhill but fairly long hike. Easy. Drop steeply down the west side of Phillips to Clear Creek. You'll be down in about an hour. Get some water and take the good program. Then head down the trail to Porcupine. This is a pleasant hike down the valley and Porcupine camp (spread for a half mile along the Rayado Creek) is a nice camp. Fair fishing.
Beaubien: About a mile downstream from Porcupine is the Philips Junction commissary. You will need to pick up food. You can then take the easy hike up to Beaubien. Relax, take a shower, wash clothes. This is a good but very crowded camp.
Beaubien layover: You can take a horse ride, lounge around or take a side hike. Good side hikes are Black Mt. (1/2 day) or the tough climb of Trail Peak (a little over half a day).
Fish Camp: Back to Philips Junction, pick up food and take the pleasant and easy hike down to Fish Camp. This is a beautiful camp and the fishing is good. Be sure to tour the cabin.
Abreu: The hike down the rimrock trail is interesting and easy. Watch your footing, and be careful if you go off the trail on your left side as it is a steep drop to the river below. Just before Abreu you will drop down to the river at Old Abreu camp. Continue to Abreu about a half mile down the river. Good camp.
Urraca: There are several ways of getting there. Go up to the burro barn and along the fenceline. There are two ways to get to Urraca. The fast way (you will be trail hardened and it won't be too bad) is up to Toothache Springs and over the top of Urraca Mesa then down the other side to Urraca. The longer way is to hike up to Stonewall Pass and take the road up to the top of the mesa. Don't like this route as road walking is boring. Urraca Camp surrounds a pleasant meadow.
Miners Park: Again there are several ways there. I would take the road down the hill to the north of Urraca. From the meadow below Urraca I would follow the trail west around the north side of the mesa to the head of Lovers Leap Meadow and campsite. There is a trail there that crosses the jeep road and enters the back of Miners Park. Miners is a pretty campsite in the Ponderosa Pine. This is a fairly long hike but not difficult.
Base camp: A fairly long hike. Head up and over a low pass, dropping down to the north fork of the urraca creek. From there it is 16 switchbacks to the top of Shaefers Pass. The only water possibility between Miners and base camp is the Pass spring. It is up the grassy slope to your left just as you enter the pass meadow. The hike up Shaefers Peak and along Tooth Ridge is rocky, hot and difficult. A new trail is being built which will make it better. When you get to tooth ridge you may want to drop your packs and take a side hike the 100 yards or so to the top of Shaefers Peak. Just before getting to the Tooth the trail drops a bit down the north side to get around the rock slide area. As you regain the crest of the ridge on the east side of the Tooth, drop your packs and scramble up the Tooth peak to view where you have been. Pretty. The hike down to base camp will take a couple of hours. It follows the ridge all the way down.
Good luck and have a great time.