Your factory head unit was loud enough because of the bose amp.
With $500 what I would do, is first see what alternator you have. If its the 105 amp, I can pretty much guarantee you are going to want to upgrade it if you get an amp. If you have the 130 amp alternator, you should be fine, or at the least wait and see where this goes, and how it does. You can get a new 145 amp alternator from a good company for $150. There are alts in size 130, 140, 145, 160, 180, 220, 250, etc... and I'm sure there are a few I am missing. If you are upgrading from a 105 amp, you will need to get the matching V-belt/serpentine belt too ($20). All Gen III engines use the same alternator so there are going to be tons of used/rebuilt/craigslist or junkyard partouts that you should be able to get for 1/2 that or less. If you think about saving money on a no-name brand alt, find out two things before you do: What amperage it has at idle, and what rpm is full amperage output. If it doesn't do full output until 3,000 rpms do you plan to downshift to cruise that high? Once you know your end goal, you will know how many amps you need to plan for.
ALT
The "big 3" improves your current flow at the source. Its where your electrical mods should begin. Its increasing the size of three wires off your battery.
Batt + to Alt
Batt - to Chassis ground
Batt - to Engine block ground.
Shops will do this for $50-$75. You can buy the wire and connectors for half that if you have a way to solder or crimp them on (reliably). There are thousands of youtube vids many of which are on your exact engine bay, and should be many easy to find how-tos.
Big 3 (These first two can be done separately)
If you run an amp to speakers, use new speaker wire for those. You will need a main power wire from your battery to your amp, another large ground wire with terminals, fuse holder & fuse, rca wires, OR just buy an amp kit. This could be as little as $25, I wouldn't spend more than $50 on what you are planning. If you are piecing together, I have liked knukonceptz.com. Depending on the amp you get, your head unit and amp may benefit from having 4ch RCAs. Once you figure out what amp you want, then you will know how big your wiring needs to be.
Wiring
Speakers in all four doors are going to be 6 1/2" or 5 1/4" with a separate factory tweeter mount if you get components. If you get components up front and can swing components in the rear, I would just get the same set for the front as the back. You can get coaxial speakers, that will save you a few bucks on speakers (, and some places try to charge more for installing components). Getting two of the same sets will make sound quality even, and make getting the right amp easier. Watts are not quality, only volume. If you are piecing together, I always suggest starting with Crutchfield.com. Great support, and I want to say the price match, but not sure. You might have to shop around after you find something you like. Amazon and ebay, might give better deals, but crutchfield gives 3 months support on anything you buy from them, wiring schematics, install tips, phone support, and they included the little odds and ends usually for free.
Speakers
When you figure out what speakers you want, find an amp that is the correct channel (4 channel, or 2 channel if you get low wattage coaxials instead of matching for the rear doors). Match up your wattage to your speakers, and your resistance/ Ohms, (will most likely be 4 ohms). There is RMS and PEAK output. RMS is your constant steady music level. Peak is your cranked up, heavy note hitting beats Peak. RMS is FAR MORE IMPORTANT than peak. Quality in an amp is less distortion, better materials so they don't overheat and last longer. I would expect $100-$150 for a NEW amp. You can find used amps everywhere if you wanted to save some money on that, as all stereo equipment you never know how well it was taken care of or abused (handled, hooked up, played).
Amplifier
This is going to be some really basic stuff. Anyone who has done an amplifier before, can probably help you with this and do it in a couple hours tops. IMO, watch some youtube vids, read the how-tos. If you don't feel comfortable doing it, I would see if you know someone who has installed there own, (maybe its me, but its nice to bring someone to the dark side). Check to see if you have anyone on craigslist who will install for cheap (less than $100 for all of it), if you have any local car clubs, (even cruise on a Friday or Saturday night for a group in a parking lot). Shop prices are going to be ridiculous for what they are doing. For two sets of speakers an amp, and big three, shops will try to charge $300+. You might even find a package deal on craigslist if you are cool with used. They might even help with install. Your best option if you haven't found anyone yet is to see if you have any shops locally that do $1 install if you buy your equipment from them. This can definitely be worth it even if you have to spend a few bucks more.
Figure this all out before you spend any money anywhere. Anyone who installs it, ask them how they will install the amp, (whether or not, they will mount it to through the floorboard or not, and ask yourself if you are cool with that). We may still see some holiday deals around before and after Christmas at shops doing cheap installs. There is nothing difficult or unusual about doing an install in these compared to any other vehicle.
Even if you don't feel comfortable wiring up the amp, and pay a shop a high price to do it; I would install the speakers, and run new wire to where you want your amp mounted. Leave an extra foot or two, because wiring sticking out from the amp, may change the direction you mount it. Then you are only paying for an amp install.
Install
Take a few minutes and here is some information about a subwoofer if you might be interested.. If you are; its either a 5 ch amp now, or upgrading with another amp for the subwoofer down the road. The 5 ch amp would be cheaper, but its more now, and probably out of the budget. Either way, plan for your end goal (electrical, wiring, amps, are cheaper and easier to do it with the complete goal in mind if you do it from the beginning. Any serious subwoofer setup is beyond a $500 budget. It might get you to buy a larger alternator now, (Example, spend $30 more now on a larger alt than what you would have used, or $200+ on a slightly larger third alternator).
Adding a sub
https://www.tahoeyukonforum.com/threads/subwoofer-options-without-losing-cargo-space-swb.107846/