Starting Strength was a good program 20 years ago, back when the closest things to scientific research was whatever strength coaches put their athletes through and blog posts on bodybuilding.com - but we've gone a long, long, long way beyond that these days. It's what I got my start on when it came to lifting, and I had good success with it back in the day, but I wouldn't ever recommend it to anyone these days.
Starting Strength is primarily focused on strength training for athletes, and the strength training you do in support of playing some other sport is different than the goals most people on this forum, so even if it still was in line with the research today, it's not the best fit.
Most people are going to be interested in a more hypertrophy focused workout - that is, building actual muscle mass. That's what will help fill in loose skin and make you more 'toned', burn (a little) more calories, etc. With this you generally want to work with lighter weights, in the 5-30 rep range. The movements/lifts you choose to do depends more on your goals and the amount of time available to you, so it's hard to make generalized statements. There are some barbell movements that are covered in starting strength that are still great options for compound movements hitting large muscle groups all at once, such as squats, deadlifts, bench press, etc., but there's a lot of muscles that will see better results with more isolated lifts.
We've got a ton more understanding these days on the minimum effective dose when it comes to volume of lifts per week, plus more science showing that focusing on the lengthened portion of the movement, even for partial reps, being the most important for hypertrophy. Working close to failure is important, but actually reaching mechanical failure likely puts too much systemic fatigue on your body to be the most efficient manner. You're still likely to get there at times when pushing close to failure, and that's fine, but it's not something you should aim for.
As for being sore, it'll always be at it's worst when you're training a muscle for the first time (ever, or after a long time off). If it's just your muscles being sore, then you generally want to stick to the schedule and push through it. It gets better after a while. Getting enough sleep, enough protein, etc., is some of the biggest parts of recovery, so also make sure you're good on these fronts. If you're pushing yourself as hard as you should be for maximizing improvement, you're always going to be dealing with some soreness, but the debilitating several days of feeling like you can't move your legs/arms/etc. should go away as long as you are working out consistently.
if you are experiencing significant joint, etc. pain, and not just muscles - that's another story. Either within the lifts or during the recovery period, significant pain there is a warning sign. A little bit of discomfort is to be expected, and over time your tendons and ligaments and such will also strengthen as you exert more force on them, but if you're waking up the next day and it's joint limiting your mobility, it's a warning sign that you're using too much weight, there's an issue with your form, you're overexerting yourself, etc. - something is going wrong.
Re: Machines, they've gotten much much much more acceptance even from the powerlifting community over the years. I would caution that they're really not that much safer when it comes to injury risk. They mitigate some risks, do nothing for quite a few of them, and introduce new ones - if you get yourself pinned doing a bench press or similar on a smith machine where you can't rack the weight, you're in a much worse position than if you did with a barbell - you can't dump the weight off to the side with the machine.
