Labradoodles can have a whole range of different coat types, depending on how much poodle and how much lab they inherit. But the good news is you don't really need different clippers for different dog breeds.
I've been happy with my Andis UltraEdge 2-speed. I wouldn't call it inexpensive exactly, but mine has lasted about eight years, and I'm only just recently considering replacing it (and a large part of that is the fact that I brought it with me when I moved overseas so now I have to hook it up to a transformer to use it). IMO a good clipper is one of those things worth going a little higher quality if possible, because a good one will last and pay for itself very quickly, sometimes in only 2-3 grooms depending on what your local groomers would charge for a clip, haha.
It's worked very well for my two curly boys, easy to clean and change the blades, and gets through thick (but regularly combed/brushed) hair quite nicely. My two complaints are that it's a little heavy for me when I have to use it for a longer groom, and the cord can be awkward sometimes, but I've yet to find a smaller and/or cordless clipper that can do the job half as well. I do now have a smaller, cordless clipper for more delicate or awkward spots, like feet or sanitary (butt and genital) trims, but it's not great for large areas of super thick or long hair. The UltraEdge was my sole clipper for many years and did just fine.
Some random points:
Definitely buy an animal clipper. The human ones are cheaper and therefore tempting, but they are not up to the job.
Take care of the blades, they'll last way longer. That means oiling after every use and storing things carefully. A good cooling spray isn't a bad idea either, because it means not taking as many breaks because your clipper blade is too hot to be comfortable on your dog's skin.
A nice set of metal snap-on combs is a great, lower-cost way to get a range of lengths to work with. Metal tends to be easier to use and more effective than plastic comb guards. I started with this set: WAHL Stainless Steel Attachment Combs Kit for 5 in 1 Blades | Chewy (Free Shipping)
but I'm sure there's others out there too. I do prefer using actual blades of the lengths I use the most, but these allowed me to buy them one at a time, when I had the money budgeted and knew which lengths I liked best.
Keep up with combing and brushing between clips, right down to the skin. A dog with a matted (actual felted hair) or impacted (really dense, packed together hair) is going to be harder to clip, even with quality clippers, and be harder on your machine and blades. Even professional groomers will often just have to give up on these coats and trim the dog super short all over, because the other option is to try to comb or brush out all the hair beforehand, and if it's bad enough that can be really painful and stressful to the dog. Better to never let it get that bad in the first place.
Also, try to use the clippers on clean, dry hair only. We don't have a dryer, so we'll often bathe and thoroughly comb out our boys the day before, then trim the day after, though sometimes if we plan well enough we can bathe in the morning and have them dry in time for an afternoon clip. This will also help your clippers and blades last longer and perform better.