Welcome to FlyerTalk, chicagoariel!

If you travel on cheap fares, basically the "tipping point" for status is going to be 25000 flown miles on a given airline (and/or its partners) in a calendar year, or (at least in the case of AA) 30 segments a year. 15 roundtrips is at least 30 segments (and a roundtrip that involves a change of planes in midpoint is more segments as long as each plane has a different flight number), so if you did all of those, say, on AA then you would have Gold status.

At AA (and at AA only) you can Challenge to get to Gold faster if you expect to fly 10000 miles (at cheap fares) within a 90-day period. See the sticky about Challenges in the AA forum for more details.

You mention your interest in lounges, though. Entry level status does not give you access to lounges, and even the next level of status (requiring twice as much flying) only gives you lounge access on days that you're flying internationally (at least at AA). AA Gold, however, does entitle you to a discount on membership to Admiral's Club lounges.

Of course, if you don't stick one airline, you don't have access to that airline's lounges anyway, even if you bought membership, if the lounge isn't in the right concourse at the termainl (ie, if you have to recross security, do a long trek, and can't get info about your flight on another airline in the lounge you're in, is it much good?). So if you think you won't necessrily stick to one airline, you may want to look into Priority Pass, which is a program that gains you admittance into various lounges. Depending on your travel destinations, it may be better or worse...

But if your main goal is lounges, be careful about "using miles to gain access to them". Even if you can do that, it's not necessarily as good a value as if you just paid for access. If you have to spend more on the fares that get you access than you would have to pay for paid access, is there a point (if you don't value things like exit row reservations and priority boarding and some chance at upgrades, which are the perks of entry level elite)?

Meanwhile, the issues with JetCheap are more than just miles. There is some benefit, beyond miles, of using an airlne you're familiar with and reasonably trust, or perhaps a more convenient airline (after all, if you're near MDW, you're near a major hub for the original JetCheaps, Southwest!). If JetCheap is someone in that category, then it may be just miles, but often there's other factors.

Meanwhile, if you're trying to get to a threshold (say, 25000 miles or 30 segments for status), then the value changes radically depending on how much you need that paritular flight to get to that threshold, and how much your value reaching that threshold. (That's why you see all the discussions around FlyerTalk about "mileage runs", flights people trying to re/qualify for elite status take for no other purpose than to earn the miles to get them to the threshold, often flying to somplace and turning around then flying right back! But they're usually doing this for elite status higher than entry-level, where the perks are richer.)

I recommend you consider setting up a spreadsheet, to calculate how many miles and segments you'll earn in a given year. You can put in actual flights you've already taken on an airline, and you can easily plug in various flights you're considering taking and have the spreadsheet automatically update the sums that you'd accumulate with a various number of flights to LGA, SFO, CDG, etc, etc. That'll give you better handle of how much you might expect to earn if you stick mostly to one airline for your typical travels. And if you do end up pursuing elite status with an airline, it'll be very helpful for tracking your progress in a year (so that you'll be able to see when you get to the point where you can afford to take some JetCheap flights instead!).

On bumps, the airlne will give you all the details prior to you securing the bump. Now, obviously, they can only give you the details as of that moment. (Say, they tell you're guaranteed on the next flight of the day, which is the last flight of the day. Then when that last flight gets there, there's a mechanical problem with the plane and they cancel it. In that rare case, obviously, you might not get out that day, just as the people who originally were booked on that flight won't.)