Weight loss comes from a calorie deficit. You can lose weight with zero exercise, if you were so inclined.

I started SL 5x5 when I was on a deficit. I'm on maintenance now, but lifting on a deficit did not hinder my progress and lifting did not hinder my weight loss. (If either were impacted, it was minimal and not really worth noting.) I would say start with 5x5. It allows you to really get comfortable with weights and work on form. Start with light weights so you can make sure you have your form down before the weight gets heavy.

There is nothing wrong with 3x5, but that is more for when you've gotten to a point of stalling. Since you'll be a "newbie," you'll make some pretty great gains strength-wise following 5x5, even on a deficit. If you get to the point where you aren't progressing, that would be the time to switch to 3x5.

As for cardio, it's up to you. I run, ruck, and ride a lot, but those are sports I participate in. At first, it was hard to do cardio and lift. My legs were tired from lifting, then not fully recovered from cardio. It took a few weeks to get it all figured out and to a point where I wasn't hurting lifting because I was doing cardio nor hurting my runs because I was lifting heavy.

Also, cardio may help you lose a little faster, but if your diet isn't in check it won't do much. (Trust me, I tried to outexercise a bad diet and got nowhere.) First priority for weight loss is to make sure you are weighing and logging all food accurately to get yourself into a deficit.

Exercise (cardio and strength training) is for body composition and health while your diet is for weight loss.

The 3x5 is sometimes recommended but I did 12 weeks of SL and all on a deficit just fine. Since I hadn't lifted in years, it was easy enough to keep gaining strength. Now that I'm using NROLFW things have slowed but there are also different lifts, ones on one foot, and a variety of rep ranges along with having been in a deficit pretty much since start of September.

So, you could do either. You want to get enough fuel for the workout but still have a deficit as the nutrition is what is the real factor for weight loss. I'm almost to overweight for my height instead of obese. The big reason is calorie deficit. Fitness helps but those are also more for other goals. I like lifting and want to lift heavy weights plus there are still some lifts I want to learn. I do cardio to reach other goals. Right now my goal is 5k and I might add a 10k jogging goal later, just to say I've done it. I also want to kayak some day. Having non-weight goals helps keep things going and to have progress even when the scale is being annoying.

Oh yeah, the cardio. I do three days of cardio, which is jogging as I'm training for a 5k, and 3 days of lifting using the New Rules of Lifting for Women program as I'm on stage 4. My schedule is:

Monday - cardio
Tuesday - weights
Wednesday - cardio
Thursday - weights
Friday - cardio
Saturday - weights
Sunday - rest day

Right now my day off from work is Thursday but that changes every now and then. When I first started lifting and doing Stronglifts, I was walking almost every day as cardio and would sometimes walk a little after lifting. I wasn't quite physically up to jogging at that time.

I started with 5x5 on a deficit. I was fine to start with. I did it for about 4 months. Once I got past the newbie gains though, and starting lifting at my max every workout for 5x5, I found it exhausting (mentally and physically) and felt like I wasn't progressing well. I might have done better with a smaller deficit, but I am impatient :P Now I am doing 3x5 with accessories.