Getting dizzy looking for a good high-chair!

Easy! Don't get a high chair. Get a Fisher Price Healthy Care Booster Seat, or something similar. It straps to one of your dining room chairs, so it doesn't take up space in your dining room/kitchen, and it will be usable for years. It is adjustable, so it grows with your child, and you can take it with you when you travel. We love ours! 

We really like the cheep Ikea high chairs. They are great. Lightweight and easily packable. It's not a chair that you can leave kids unattended in. But it has worked great. Cost is about $15. We take it camping and travel with it during local/car trips. 

-Bill

It's no frills, but compact, easy to use and cheap.

http://m.ikea.com/us/en/catalog/products/spr/89228434/

Ikea. Seriously.  It's simple, compact, and easy to clean, and you can skip the tray later and use it as a higher chair at the table.  We had an expensive one but got rid of it in favor of the IKEA one, which was $30 or something like that.   

I have 2 toddlers...we've never had a traditional high chair, we have just used this clip on chair on our dining table: https://www.target.com/p/inglesina-fast-table-hook-on-high-chair/-/A-15…

We're big fans. Doesn't take up space, portable (we even have a second one in our car to bring in restaurants as our babies always seemed happier in it than restaurant high chairs), it's nice to have everyone at/eating on the table - makes it feel like a real family meal. You can remove the fabric and wash it in the washing machine pretty easily.

In our case we have been able to use it from when they first start eating real food until past 2 years old, when they've been ready to move to a simple booster.

We had all 3 of those needs and the Graco Slim Spaces series was a great option for us. We folded it up after every use. https://www.amazon.com/Graco-Slim-Spaces-Chair-Manor/dp/B00H8MSFE6/ref=…

I know the Stokke is pricy, but we LOVED that chair.  My son is 95% for height and only just stopped using it at age 8.  I was able to resell it for about half of what I paid.  Totally worth it.

I Have this one-  https://www.amazon.com/gp/aw/d/B009MMK8MC/ref=mp_s_a_1_2_a_it?ie=UTF8&q…

it folded up easily, tray and seat easy to clean, and wasn't terribly offensive looking. I have it in black. We're done with it; happy to sell it for 50 bucks if you want it! 

Lgshamszad [at] gmail.com

Stokke Tripp Trapp is great! Tray is sold separately though - I found one on Craigslist that is larger than the one you can buy online. 

I recommends the Fisher Price Healthy Care Booster Seat (~$20). It's plastic with a dishwasher safe tray, extremely compact, indestructible, extremely easy to clean, and easy to travel with -- restaurants, camping, vacations, etc. It straps to an existing chair (or picnic bench), when you're not using it, the seat back folds down so the chair can be pushed under the table (making it not visible when not in use), and you can remove the buckles and turn it into a regular booster for the dinner table when the time comes. I have a couple and they've lasted over 5 years through serious abuse. My kids have outgrown them, but I keep them around for guests with little ones because they're so compact and easy to store. Cheap, durable, and so much more practical than the fancy high chairs that take up a lot of space and are nightmarish to clean. And, at $20, if you hate it, put it on the curb for free and it'll disappear.

How old is your child?  We used the $15 Ikea high chair when my daughter was just starting solids.  It's a breeze to clean. But the tray, once snapped in, is hard to remove.  This wasn't an issue for us because my kid is a skinny string bean and I could just slip her in. You can get cute accessories (like cushions in wipeable fabrics and custom fitted silicon mats) on Etsy.

When she turned 1 year old, I got the Beyond Junior Y chair, which I really like.  It has a 5 point harness, so it can be used for infants as well.  It's made of wood, and has easily removable cushions and a compact footprint.  It's relatively easy to clean.  The wooden tray has a clear plastic cover that's easy to wipe down snap off to wash.  But the tray itself requires 2 hands to install and remove.  IMO the tray could be bigger.  The seat and footrest adjust to grow with your child for several years.  Warning, there is a removable post at the crotch that helps keep little ones in the chair, that tends to collect food particles.  I used an extra big bib that draped over it, and then eventually removed it when my kid was stable enough to keep herself seated upright.

Also tried the Oxo Tot high chair which looks beautiful and modern and seems super comfortable for kids, but was horrible to clean.  The plastic components (seat and tray) have a matte texture that holds onto purees and sauces, and the belts on the chair we got were extremely difficult to remove for washing. I got downright angry at every cleanup, and sent it back after a couple of weeks.

The Inglesina one that attaches to the table served us well.

Not sure if it meets your compact standard, but we love our Oxo Tot Sprout, especially for your first two asks.
The 4moms high chair was the other chair I was considering- the tray is super easy to get on and off, but we thought it would be too hard to deep clean, and the magnets really aren't very powerful.

JOOVY Nook High Chair. 

Amazon has good reviews to take a look. Our girl has had it since she could sit up. Watch the product video.

We love our Stokkes.  (You can find them used often on CL- up to $200- there are a couple on CL now- but we've paid less). You can get an insert for infants (and there's even a huge, huge tray that goes with it, made by a 3rd party (thick translucent plexiglass). It's an airport it's so huge, easy to clean).  There are straps that go with it, but their not that great IMO. I just made one myself to keep our toddler from climbing out.  Why is it so nice?  Our 5 yo is still using his.  It totally adjusts as your child grow.  Have a look. They were everywhere in Munich one time we visited (cafes, bars, people's homes), so we came back and got one. Very pleased.