Hi Ginger. Okay, this may sound a bit harsh, but it isnt a good sign that you "arent willing to spend the money". You CAN create your dream, but loosen the wallet a bit, cause its not going to be cheap. Realize that about 1/3 of what you plant probably wont make it a year, then you will get an idea as to how much it will cost for plants alone. Add in cost of soil and irrigation, and then make a budget. Start acquiring plants early, and get them used to their new location and you will have greater success. Beyond that, read a lot and get ready to spend some time on the thing, then you can create what you envision.
DD

Your dream yard looks doable. In fact it looks like my neighbors yard except they have a pool where your grass is. DD has the right idea about slowly buying your plants and letting them get accustomed to your microclimate. You can buy smaller (cheaper) plants and give them time to grow before planting. I've been buying plants for the past 3 years and I'm at the point of running out of room so I'd better start to plant these babies.

One thing you can do, plant things that grow fast.Bananas and cannas come quickly to mind in your zone, especially bananas and cannas with fancy leaves like zebrina banana, and tropicana, or pretoria canna, or any of the red leaved varieties. And space them a little further apart. Fill in the gaps with cheap annuals for a few years. A crepe myrtle might be a good plant to take up some room/provide some bloom. Daturas and brugmansias are pretty cheap too.
I'd recommend some of the amaranth family plants. They will reseed themselves, some of them are red and tall,some are tricolored, some like the "love lies bleeding" have nice dangly hanging ropey tassels, and they will all fill in quickly. Another good one is the perilla frutescens. This is another one you can grow from seed (it will take over, though!) and it will provide a good deep purple color.It can take sun but looks like a tall dark purple coleus, up to 36" tall.cut and paste this link in your browser. The perilla is behind the waterfall, and it's not full height yet in this picture.

http://image52.webshots.com/152/1/58/78/458715878kaYgLt_fs.jpg

The amaranth is the large red plant in the left center of the other url picture below. I planted it a few years ago, it drops seed and comes back and you can transplant it and thin them out so that they aren't so crowded.
I'd add a few hibiscus too. They will soon take up a lot of room.
On a sad note, I don't like the "after" picture. It looks too artificially lined up and not "jungly" enough for those kind of plants. Also, it's overplanted. When those plants grow, it will be just a solid block of leaves. Delete about one third of those plants to allow for growth, which is also good for your budget! and stagger planting lines and make it look more natural. Also plant tropical looking annuals in odd numbers, to fill in for the meantime, for best effect. New guinea impatiens, celosia, nemesia, sun coleus varieties, ornamental sweet potato vines. Variegated spider plants (airplane plants) from hanging baskets make great temporary filler plants near sidewalks for borders and are so cheap. There are surely lots of others that your consultant can recommend for your area.
Plant bananas and cannas singly since they multiply so rapidly. Gingers will multiply fast too. The large basjoo banana clump in my picture in the link below is only three years old, and that's in Indiana, so you can see you will need to allow at least 7-8 feet for a clump size in three years.I only planted one 9" plant.
I hope this is helpful.I'm not designing a lot of beds around here right now, so I had fun with this.

Sandy

Here is a link that might be useful: {{gwi:1303723}}

I agree with Sandy. She seems to have a good aesthetic sense... Unless you actually want the formal garden look in which case you may want to consider plants traditionally used such as boxwoods.

What I'd add to Sandy's comments: You may want to ease the rather stark transition between the concrete path and the far planting with a row of uniform groundcover like Liriope or Monkey Grass. This will help unify the whole and mitigate the "hodgepodge" appearance.

Also, consider the concept of recurring themes: If you have, say, a Pheonix Roby Palm flanked by orchids in a certain pattern, consider doing it at two opposite corners.

The challenge before you is that your layout is not formal/symetrical (by far the easiest landscapes to design), so you need to overarch the chaos of jungle with some order, yet not stiff order. This is where professional landscape designers earn their $$$.

You can't really be too overgrown with this theme. Take a look at the real rainforests and jungles; that's the way they are. You'll need to vary the form, using palm trees to mix it up, lots of big leaf plants, and different textures. Bamboo really adds to the effect, but do your homework before planting.