Does the iPhone 4 really run such an outdated version of iOS that it can't run most/all of the popular apps out there?
Yes, it no longer receives security patches or OS updates. Planned obsolescence, just like the rest of the fargin' iOS line.
What open security bugs are there? Are they actual serious ones, or the "if you hand someone your phone, they can wreak havoc on it" kinds of bugs? Is it vulnerable to the "plugging into a hacked charger" issue?
I couldn't find a list of security issues that were still present on the 4. All I could find is a security patch issued to it February of last year. So I dunno.
I don't expect it to get the latest OS. In fact I'd kinda prefer it didn't. I've heard the iPhones tend to get slower and slower as they get upgraded to newer and newer versions of iOS. I'd prefer they get upgraded once or twice, then just security patches past that point.
Anyways (and yes, I know that's not the correct spelling!). Here's what I recommend, in my personal order.
* Moto G for $79. I won't link to the ebay auction, but I see one with a title of "Motorola Moto G XT1031 *Android* Cell Phone Sprint GOOD TO GREAT 187923" that is $79 free shipping. This runs a recent (possibly the most recent) version of Android. It'll do the majority of what iPhones can do, ESPECIALLY if you're not a power user. The main issue I see is everyone using iMessage and you won't. IF you can get them to install another messaging app (such as Viber), then problem solved.
* iPhone 4s. I see several ebay auctions around the $100 mark. In fact there's one that ends in less than an hour, no bids at $75. Buy it Now is $110. Free shipping. Several under $100. Just be careful, you have to read the description that the seller puts in (which is underneath the ad-text telling you about how awesome the phone is and all the specs, maybe a video which is generic to ALL phones of that type). Look out for "BAD ESN", "Locked", "iCloud Issue/Locked", "Cracked screen", "Not Working", etc. In fact, if it says "iCloud" or "See Description" I immediately skip the listing and don't bother looking at it.
* iPhone 5c. I see them around the $150 range. One particular auction is $155 buy it now with free shipping. It doesn't come with charger, so add $10 or so for that (if you already have a usb charger, just buy a decent iPhone cable for a few bucks).
* iPhone 5s. $200 and up. Be careful because a lot around this price range have issues (not because the 5s is a bad phone, I'm saying a lot in the $200 range have a bad esn, and/or cracked screen, and/or iCloud locked, and/or....). I see one that is $200 plus $9 shipping. Fair condition. Does have dreaded "iCloud" word in description, but it's to say "iCloud has been removed" which is a good thing.
Whatever you get, make sure it's from a reputable seller. Pay using PayPal, and choose to fund using a credit card. Any issues, a reputable seller should make it right. Still have issues? Dispute with ebay and PayPal. STILL have issues? Contact your card company. So far, I've never gone beyond an ebay/PayPal dispute, and even that's rare.
Oh, and of course, if you must have Sprint, search for Sprint in the title. Verizon, Verizon in the title. T-Mobile or AT&T, it could have either in the title and say "Unlocked" and you'll be fine, though you may not get the fastest 4G available (if you're on prepaid, you probably wouldn't anyway).
Now, if it were ME, I would pick a Moto G for Verizon (have to be careful, MOST of them are prepaid models and cannot be activated on anything but a Verizon prepaid plan...this includes NO MVNOs). Check the MEID, make sure it can be activated on Tracfone's BYOP plan. Costs $5-$10 to activate, then $20 per 90 days for 180 minutes, 180 texts, and 180MB data. That's enough for light usage. For an iPhone, I'd pick the iPhone 4s, same plan (anything newer is 4G and takes an LTE sim card from Verizon, which does NOT work with Tracfone's BYOP plan). But shhhhh, don't tell I.P. Daley. He hates anything related to Tracfone, and his reasons aren't completely unwarranted. I'm willing to sacrifice some sanity in exchange for a few bucks.