If you're buying your first motorcycle chances are that it's a cheap used bike. Chances also are that you've seen a motorcycle only a few times ever and don't really know what to look for.
This is a quick guide covering my approach to buying cheaper used bikes, which should work well for a new rider. Realistically speaking, you're probably looking at a $500-$2500 bike, not a $50,000 Porsche, so you don't have to go too crazy about checking every detail.
If you're experienced in buying used cars, you can just skim this, because the approach is pretty much the same. TL;DR is that if it looks/feels like a POS, it probably is.
Note that this has nothing to do with *which* bike to buy. That's personal and specific and you probably will (and should) buy the wrong bike your first time out.
How much you should spend depends on a lot of factors such as what kind of bike you're looking for, where are you located, how old/new a bike is. But here are some general numbers to give you an idea
Whatever your budget is, include $500 on top of the cost of the bike for maintenance and customization. Even with a new bike you'll often need things like a skid plate, hand guards...etc.
Make sure to budget for basic gear. See Starter dirtbike gear guide
In the US, a decent used offroad focused motorcycle (dirt bike, enduro, or dual sport) will typically run you $1500 - $3000 at the lower end. Anything cheaper than that is either a screaming deal or a piece of junk, the latter being more likely.
You can save yourself a lot of time by looking closely at the ad, usually this will sort out 90% of crap. Often a half assed ad speaks to the character of the owner and their approach to maintenance. Things I look for:
Multiple pictures that are not a screenshot of the picture on the phone. In which I look for:
Significant rust or corrosion
Sagging chain
Leaking forks
Missing or seriously damaged body parts and missing fasteners
General jankiness
Decent description including mileage and/or hours.
Title status, I would ask about this if not mentioned. Not having a title is pretty common for older off-road only dirtbikes, but is somewhat annoying to deal with.
Responsiveness and character of the seller.
Specific maintenance details (such as valve clearance checks) are a big bonus. You can look up the maintenance schedule for the specific bike and ask the seller about it.
When you go look at the bike, I usually look at the following things. None of these are a deal breaker, but unless you're specifically expecting to have a "project", some of these can be a significant cost to address.
General "feel" of the condition. Does it look beat up? Does it look poorly taken care of? A bunch of scratches and dents are expected, especially on an off-road bike, but scratched and broken are different things.
Engine
The bike should start easily, hot or cold, and idle well without stalling. If it doesn't, it can mean anything from a weak battery, to a dirty carb, to a engine needing a rebuild.
Looking under/around the engine there should be no leaks of any fluids. Some gasket seepage and two stroke spooge is ok on dirtbikes, but there should not be any actual leakage.
Check the radiators or oil coolers for straightness. Many dirtbikes will have them at least slightly bent, it's okay as long as they're not leaking and the bike is priced accordingly.
Ask to see the air filter... as long as it's there you're probably good, and if it's decently clean, that's a great sign. Bikes used off-road dirty their air filters very quickly, so if it looks dusty it's okay. If the seller doesn't know where it is or how to get to it, that's not a great sign.
Look at the chain - if it's rusty, makes rattling noises when you ride, or if you can pull it off the middle of the rear sprocket (the gear thing on the rear wheel) by hand by more than a 1/2 or so, it will need to be replaced. Very common with a used bike, but something to be aware of.
Any loud rattling or clanking is a big red flag. If it sounds broken it probably is.
Suspension
No leakage from the forks or the shock. If there is visible oil on any of those, the seals are leaking. Sometimes cleaning them will help, but likely they will need to be replaced and fluid changed.
Sit on the bike and bounce up and down. The suspension should compress and rebound without any clanking, weird noises, or feeling of something being loose.
Sitting on the bike and holding the front brake push the handlebars forward and back and rotate them lock to lock. They should move smoothly and there should be no back and forth play or clanking sounds.
Controls
All levers and pedals should be reasonably straight and usable. They're cheap enough to replace, but if a bike is being sold with broken off controls it's a huge red flag and should be priced accordingly. They may not be adjusted to your liking and it's fine, it's a personal preference thing.
The clutch and throttle should operate relatively smoothly. This is not a deal breaker since it's something nobody maintains and usually only takes a little bit of lube to make them perfect, at worst the cables are cheap. If the throttle doesn't snap closed on its own you'll need to fix it before you ride though.
Bodywork
For a cheap offroad bike, expect it to be at least somewhat old, well used, and maybe even broken... but it should at least be there. Plastics can be surprisingly expensive.
Look up what the bike should look like online. Some people remove lights off of enduro bikes and replace them with number panels. Make sure to ask the seller for those parts if they have them.
Tires, wheels, and brakes
Make sure the tires have air in them before going for a test ride.
Run your hand across all the spokes and make sure all of them are there and none are loose or bent. Loose spokes can usually be tightened, bent spokes would need to be replaced. One or two are not a deal breaker, more than that and the wheel will be very out of true.
Check the brake pad wear. Worn brake pads are cheap and easy to replace, but if they were worn out a year ago they may have worn out the rotors, which are not cheap.
Many trail and dual sport bikes will still have the original tires on them 10 years later. Those will be dry rotted to hell. Not a deal breaker, but plan/budget on new tires, tubes, and rim strips right away.
Lights and such
If it's a street bike make sure the lights work. Most common thing to not work are the blinkers and the brake light (should work with either brake). Easy but time consuming fixes.