Well I got the sore muscles out of my system from my beginner time skating in circles in hockey skates. I like lifting weights for skating (squats, deadlifts, and Olympic lifts) as they really strengthen your anaerobic capacity a lot, and putting a 200lb weight on your back and going down and up a few times makes skating seem like a comparatively easy activity (sorta, it's mentally quite tough.) Basically, muscle soreness is part of the game with any athletic activity. You break your muscles down and they rebuild into stronger muscles. So you either accept soreness now or stay home and get clogged arteries. Obviously there's a breakeven point, and different people have different inate capacities for stuff. For a weight training program, probably one of the better ones is Mark Rippetoe's "Starting Strength" program, it's a good beginning program. As far as bulking up on it, most females can't gain a lot of muscle due to low testosterone levels, a male will usually struggle to put on about 10-15lbs of muscle a year, so a woman won't usually put on over 7-10.
Nutrition might be a bigger issue for you, too. Lots of women in my opinion really undereat, either because their appetites are naturally low, or because there's lots of concern with their aesthetics. Generally the recommended amount of protein for an athlete is about 1g
per pound of lean body mass not per pound, but get your bodyfat measured, and let's say you're 20% at 110lbs, you need 88g a day. Protein isn't *everything* but protein is needed to rebuild the muscles to be stronger. You can rely on shakes and stuff for it, but it's better to try to get it from food and have 3 balanced meals a day. Also, you can possibly eat a bit more (don't go paleo/Atkins kinda crazy with this) fat in your diet, as your body needs saturated fat and cholesterol to make hormones, and Omega 3s are needed for brain health, and Omega 3s have a bonus of being anti-inflammatory. As far as calories go, you should probably have more. At my bodyweight, skating an hour supposedly burns 700 calories. So you do more cardio, you burn more calories, and if you're trying to lose weight, that's great and you gotta do what you gotta do, but at the same time, if you cannot perform how you want, then it's time to up the food intake. As a woman, you don't gotta go insane with this (as a guy I sorta kinda can) but you should have at least 2000 calories a day if you're skating that day.
As far as supplements, you can't rely on NSAIDs like ibuprofen/tylenol, that's a bad bad shortcut, as they're very liver toxic if used prolonged periods of time. Some people are insane and use them anyway everyday, but it's not good to rely on that. Fish oil is naturally anti-inflammatory, turmeric is too. You should be ideally taking a multivitamin, and possibly supplemental magnesium. Plantains and bananas are very good, as they contain potassium, and potassium helps your muscles not be sore, it's why Gatorade/etc has it, and other electrolytes. Lastly, creatine might be an OK option to supplement with, if you don't already have a lot of meat in your diet. Your muscles need creatine to fire, and it can only be synthesized from meat. Type II (fast twitch, ie, jumping) muscle fibers require creatine to fire, and Type I (slow twitch, ie, marathon running) are the ones that use glucose. So creatine, you pretty much don't need if you do eat a decent amount of meat, but if you don't eat meat or rarely eat it, it's an option. That's very generalized nutrition info, which is all I'm confident enough to give you.
Lastly, for cardio, if it's at all possible, just try to skate more and do less cardio on an eliptical/etc. Or, go for hikes or walks instead, as hikes and walks are much better emotionally (my opinion anyway) than an eliptical in a gym is. Again, you gotta do what you gotta do what you gotta do, and if your schedule doesn't permit walking/hiking/cycling or more skating, you can't do it, but yeah. One cardio exercise I recommend 1000% for skating is a slideboard.
That's much much better than an eliptical machine for a general workout, and it uses almost all the same muscles as skating stroking. It's sweet. Your gym may not have one, but they're able to be bought online, or made if you're creative, using either some plastic, "hardboard" (wood panelling for walls) at home depot, or linoleum, and some boards for stoppers. Eventually once you get good at the slideboard, you can hold dumbells in your hands. I generally go on the slideboard for 3-5 minutes at a time, I'll put a song on my headphones and go from start to finish with the song. Take a short break, go back on again usually 5-10 times. I feel the slideboard is probably the best prep for skating muscles, even better than weights and machines (though I do love weights.)
Lastly, as far as sore muscles go, it depends. Sore muscles aren't bad, but if you get sore tendons and ligaments, that's when you gotta back off. As long as your general day to day energy levels are good, then you're OK, assuming you can like, walk. The only really bad thing to worry about for overload is your adrenals really. That's an issue I have, I took the shortcut of consuming lots and lots of coffee/energy drinks to get through my daily life and workouts/skating. Now I can barely function without it, and my natural adrenal capacity is bad, as stimulants only trigger your adrenals on, your adrenals don't really naturally improve. This isn't just skating, but stressful life in general will do it. Also, it raises cortisol, then cortisol (at the wrong time/levels) pretty much makes you fat. Not fun. The problem is, it's not even athletic, it's more just stress in general that does it, if your life is stress free besides your athletic hobbies, then you're fine, but if your job or home situation is stressful, excess cortisol and adrenal fatigue are knocking at the door, and adding athletics to the equation can sometimes make things worse if the activity doesn't relax you/make you happy (skating probably relaxes you and makes you feel good, the eliptical machine probably does not.)
So that's my advice, as odd as some of it might sound.