Honestly, for that budget and your D3500, there is really only one choice that makes sense if you want to be happy with the results. I have been shooting with the Sigma 150-600mm f/5-6.3 DG OS HSM Contemporary for Nikon F for years and it works perfectly for exactly what you are doing. Here is why this specific lens is the right move:

• Reach: On your D3500, this lens effectively gives you a massive zoom range. Birds are tiny and skittish, so having that 600mm at the long end is essential to get close-up shots without scaring them off.
• Weight: Unlike the more expensive Sport version, the Contemporary model is light enough to carry around the lake for a few hours. I have never had complaints about fatigue with this setup.
• Stabilization: The Optical Stabilizer (OS) is very reliable. It helps keep the image steady when you are zoomed in all the way, which is huge for beginners who dont have a tripod yet.
• Price point: You can usually find these new for around 750 to 800 bucks, or even less if you look at used options, which leaves you some gas money for the trip. I have been very satisfied with the sharpness I get even at the maximum zoom. It is a high-quality experience without the five-figure price tag. Just make sure you buy the Nikon F-mount version and you will be good to go. It is a solid piece of glass that wont let you down.

To add to the point above: everyone is right about that 150-600mm being the gold standard for reach, but if you are worried about weight or blowing your whole budget, there is another way. I have spent a lot of time lugging heavy gear through marshes and learned the hard way that a lighter setup usually means more keepers because you arent fighting the lens. Summarizing the options we have talked about so far:

• The big 600mm zooms are amazing for distance but a literal pain to carry.
• Weight matters a ton if you are hiking around a lake without a tripod. In my experience, the Sigma 100-400mm f/5-6.3 DG OS HSM Contemporary for Nikon F is a sleeper hit for the D3500. It is way lighter, significantly cheaper, and on your camera, it still behaves like a 600mm because of the crop factor. You can usually find them used for around 500 bucks, which leaves you plenty of cash for a nice bag or extra cards. Just buy used from a reputable site and you will be golden.

I spent years lugging heavy gear before realizing that focal length isnt everything if it's too heavy.

• Are you using a tripod?
• How far away are the birds?