I want to be an engineer who works with microchips and things like that. Are there any small projects and things which I could do at home (spending less than $100-200) just to get a feel for things?
As stated by others, microchips and machinery are built in totally different ways. There are a number of microcontrollers on the market that give you access to hardware control while learning the software aspects, which puts off the tricky interfacing questions till later. Parallax BASIC Stamp devices and Raspberry Pi have gotten a fair amount of attention and support, the former in various robotic device projects while the latter has stronger support for communications, it seems to me
You want to be an Engineer? Dude, check out Mechatronics. Fairly new field, you'll love it.
www.okorder / first get a grip on the basics
Yeah that's one aspect of mechatronics. Perhaps borrow from the history of computer controlled machines and add computer control to a manual machine? eg a relatively small project would be to take an existing manual drill press, and add micro chip controlled motors to move the table. You'd find that useful in itself as you can then use that to create PCBs for further project work). just remember that's a drill press isn't a milling machine- the bearings on the spindle (part that turns the drill bit) won't be designed for lots of side forces- so limit milling to *very* light cuts . You'll need to get a hang at controlling motors, and programming the microcontrollers. I've found both pic uCs, and arduinos to be pretty easy , but everyone has their favourites/mileage varies. If you want to have a go at making the physical machines you wouldn't go far wrong in having a look at David Gingery's build your own metal working shop from scrap series. While it doesn't go into great detail about why parts are a given physical size,(ie it's less about engineering, and more about fabrication) it's a very useful book of patterns that you can take and develop in your own way. Quite a few people have taken the ideas in that series and added microchip controlled motors. Casting also a very useful skill if you're making your own items.
Machinery and IC's is a strange combination. As the other person said, first learn the basics, such as ohms law, resistance capacitance and inductance, and then simple circuits. You need all of that before you can even think of an IC.
