Ok, the leap from $1,000 to $2,500 is a big one.  I certainly didn't make it at one time.  It took me years.  But I know folks that decided they wanted to get into woodworking and dropped at least $2,500 getting themselves outfitted.  When you do make the jump, the thought process becomes much less about making sure you can get the job done and becomes more about having quality tools to get the job done.
The Jay's Customs Creations YouTube channel releases weekly videos on shop projects and dimensional lumber projects. Jay's show can really help you if you want to do DIY woodworking projects on a budget. He sometimes shows viewers how to complete the project without electricity and using only hand tools. He goes over the prices he paid for materials to give people a realistic budget for the project before they get started.
I can't really give a great answer to your question - I'm still learning how to deal with woodworking on a limited budget myself, but I'm getting there. It's not always easy, but when I want something I can't afford, I am starting to remind myself more and more that someday my day will come when hopefully there will be more room in the budget for my woodworking hobby. I'm also hoping to start selling the occasional item within the next year to help bring in some extra money for woodworking related expenses.
My first projects were making things from pallet boards. I cut the boards to size using my jig saw.  It’s not quite as good as using a miter saw, but it got me by for a while with sufficient results.  Even now that I have a miter saw, I still use my jig saw A LOT to make notches (like for my outdoor table), or fun designs (like these deer heads last Christmas).
Steve Ramsey makes woodworking fun. His YouTube Channel, Woodworking For Mere Mortals Building, shows Steve making cool stuff in his garage in Marin County, California. From games and toys to special holiday projects during his 12 days of "Craftmas" (wooden snowflakes!), Steve consistently puts out new DIY woodworking videos and projects every Friday.
Steve Ramsey.  He's an energetic, fast-talking eccentric whose built his channel based on projects that can be done without investing in fancy tools.  He trudges out a banged-up table saw from his garage, chops stuff up on the bed of his truck, and generally produces well-structured projects - even if I can't agree with his design aesthetic and color choices.  Lots of good stuff to learn and a great channel for someone starting out.  
Ok, the leap from $1,000 to $2,500 is a big one.  I certainly didn't make it at one time.  It took me years.  But I know folks that decided they wanted to get into woodworking and dropped at least $2,500 getting themselves outfitted.  When you do make the jump, the thought process becomes much less about making sure you can get the job done and becomes more about having quality tools to get the job done. 

Flea markets and swap meets are great sources of old tools, but unless you are able to rehab and sharpen them, they aren't going to do you much good. You can always find lots of chisels and planes at these places, and they can be brought back to life. I wouldn't waste my time on any saws though, unless they are relatively rust-free. If a saw is rusty, you will have to re-file and re-set the teeth, which requires a good deal of expertise and some specialized tools.

Then there are the “practical” woodworkers that enjoy weekend projects and things that don’t require a ton of expensive tools, time, and expertise (HELLO, THAT’S ME).  I will be in the latter category.  Sure, you can invest in hand tools, but in the words of one of my favorite internet sensations, “ain’t nobody got time fo that.”  Let’s be practical here.
Finally, at the beginning you'll do just fine with a basic set of router bits that run ~$40.  A starter set will typically include straight bits for edge matching material, a selection of edge finishing bits, and some joinery bits.  As you work on a few projects you may find that more specialized bits are needed.   But specialized bits are expensive - so purchasing them as you have a specific need makes more sense than buying in anticipation of a need.
Check with Habitat for Humanity.  If they have a store you may find several good items such as a bench, bandsaw or etc.  When I retired and moved I donated  a complete shop full of woodworking power tools and hand tools to Habitat.  They sold them, I deducted them from my income tax.  Unfortunately I could not retire my desire to woodwork and at age 78 I built a shop and use only hand tools and a bandsaw.  Good exercise pushing  a LN #7.   Build yourself a solid bench with some southern pine with a moxon vise that can be built by hand.  Get some holddowns!
If you'd like to learn more about the differences between hardwood species, I can think of no better resource than R. Bruce Hoadley's 1980 masterpiece, Understanding Wood: A Craftsman's Guide to Wood Technology. Not only does Hoadley detail nearly every species used for woodworking, he does an exceptional job at describing how to prepare, work with and finish these hardwoods. This is an industry-standard resource, one that I'd highly recommend to every woodworker.
Turn leftover wood or old pieces of furniture into DIY reclaimed wood projects! Wood is one of my favorite materials to work with. The possibilities are endless and they give such a homey and cozy feel to any rustic home. My husband, Dave, and I sometimes even go the extra mile and carve our initials on a little spot. It’s our own way of making our DIY project even more personal! Here’s a list of some of our favorite DIY reclaimed wood projects!   
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