For a budget-friendly and lightweight backpacking stove, there are a few great options that can fit the bill. The MSR PocketRocket 2 is a popular choice among backpackers. It's compact, reliable, and usually priced lower than premium stoves. Another great option is the BRS 3000T, which comes in at a very low price point and is impressively lightweight, though it may not be as durable as some higher-end models.
If you're comfortable with using solid fuel, the Esbit Pocket Stove is incredibly affordable and compact, although it's not as fast or efficient in heating as a canister stove. Alcohol stoves, like the ones from Trangia, are another lightweight option, although they require carrying liquid fuel, which can be a bit heavier.
For finding good deals, consider checking online retailers like Amazon, REI Garage Sale, or even eBay for second-hand options. Local outdoor stores sometimes have sales or clearance sections where you can find good prices on stoves.
Also, joining backpacking forums and groups on social media platforms can be beneficial as fellow backpackers often sell or trade gear. As you look, consider what type of cooking you’ll be doing on your trip (just boiling water vs. more complex cooking), as that can influence the best stove choice for you.
Have you narrowed down when you'll be traveling or what kind of meals you’ll be preparing? That might help in choosing the right stove for your needs!