advice on weight lifting routine

It looks pretty solid, with minimal overlap. Just one question - why choose dumbbells over barbells?

if you haven't lifted before, new rules for lifting for women is an awesome resource.

I do strength 3 days a week. I have 3 workouts in which each has a dedicated group of muscles rather than specific workouts. Each workout day combines upper and lower body and different areas. Ive composed a binder for myself (courtesy of Google lol) where I've collected different workouts for each muscle group.

Workout A:

Chest
Triceps
Shoulders
Glutes
Hamstrings
Abs

so I'll flip through my binder and do 2-3 strength workouts for each group. It sounds like a lot but it's not bad. And I also use dumbbells because that's what I have at home.

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I would keep the below exercises.

Squats
Deadlifts
Bench press

And add -

Overhead press
Barbell Row

All are great full body exercises. If you are just starting out, use dumbells, if you eventually want to go heavy you will have to switch to a barbell.

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I'm trying out a gym for the first time, and want to get into free weights. I've decided on using dumbbells rather than a barbell and am wondering if the moves I've chosen covers all the muscles for a full body session. If not, can you suggest some? Or tell me if I can drop a couple if they're overlapping with others. I've worn out Google with trying to piece together a program to start with. Anyway, here's my list:

Squats
Lunges
Deadlifts
Stiff leg deadlifts
bench press
Military press
Dumbbell row
Lat raises

Thanks in advance!

First, I would still recommend a Barbell for at least the Deadlifts, Squats, and Bench Press. Dumbells are fine for other exercises and this will give you some variety. Check this out. I would split that into an upper body day and a lower body day that you do twice a week.

Lower Body Day 1
A. Barbell Deadlifts: Do sets of 3, increasing the weight 10 lbs each set until the next weight increase would be too much for 3 reps
B. Lunges: 3 to 4 sets of 8-12 reps
C. Stiff Legged Deadlifts: 4 sets of 8-10 reps
**On Lower Body Day 2 replace Deadlifts with Barbell Back Squats

Upper Body Day 1
A. Barbell Bench Press: Do sets of 3 reps, increasing the weight 10 lbs each set until the next weight increase would be too much for 3 reps
B. Dumbell Bench Press: 2sets, find a weight that you can do for a minimum of 10 reps but max out the reps, press until you can't press no more. If you can do more than 10 reps with that weight for the 2nd set, grab the next set of dumbells and rep out again.
C. Dumbell Rows: 3 to 4 sets of 6 - 10 reps
D. Military Press OR Lat Raises 4 sets of 8-10 reps
E. Shoulder Shrugs: Grab that barbell or dumbells and do shrugs. Just up and down, trying to touch your ears with your shoulders, not the circular motion you see some morons doing. 3 to 4 sets of 8-15 reps
F. Do some curls: 4sets of 8-10 reps
G: Tricep work with the barbell or dumbells: 3 to 4 sets of 10-15 reps (slow on the downward movement)

I would keep the below exercises.

Squats
Deadlifts
Bench press

And add -

Overhead press
Barbell Row

All are great full body exercises. If you are just starting out, use dumbells, if you eventually want to go heavy you will have to switch to a barbell.

Yeah those 3 were my definite keepers.
May I ask why overhead instead of military press? And aside from the equipment, aren't barbell and dumbbell rows essentially the same?

Military press is harder as you keep your feet and heels together, while overhead press you keep your heels about shoulder width apart, I would certainly go with overhead press and start with an empty barbell.

To correctly row and get the best workout for your back you should use a barbell, start with the bar on the floor, pull it hard until it touches your lower chest, then return back to the floor for one rep. It is impossible to work your back properly with the bar hanging in the air which is how most people perform rows. Hope this helps