I've got somewhat of a weird situation so hear me out.

I plan on using my beater bike as a rain bike/grocery shopping bike so I was looking at some fenders... but if I get a rear rack with a top flap like this:

https://www.amazon.com/Topeak-6310703...2186246&sr=8-1

do I still need a rear fender? The reason I ask is because the road-bike type fenders I have on now are extremely flimsy, and whenever I take apart my bike to travel somewhere the fender always gets out of line. I got so pissed at having to re-align my fender every time that I just took it off. Now its raining. Great...

Unfortunately bike rack for my car isn't an option because of the odd shape of my hatchback, there's very few models (expensive) that actually work.

With only a rack you'll still get crap thown on the back of your legs and on the front from the uncovered front wheel.

In addition to what SuncoastChad said, your chain and sprockets will also get a lot dirtier. My advice is to get the rack with the RACK features you want, and add fenders anyway.

I remember when I was a kid, I couldn't get fenders, racks, and chainguards off of bikes quickly enough. Now, I don't even consider bikes that don't take them. Funny how things change.

My rear rack doesn't have a solid top, but in the winter (our rainy season) I just bungee something on top of it to act as a fender substitute. It doesn't keep all the spray off the bike, but does keep my back and rear end from getting soaked. Still need a front fender to keep my feet from getting soaked. A splash guard that snaps under the down tube can help if you don't want to have a full front fender. At least they have a concave shape so the water hitting them tends to bounce down and inward instead of outward onto your feet as it does when hitting the down tube.

The rack with the solid top is better than nothing, but not all that much better than nothing. I would try living with your fenders again. Maybe there is a better grade of fender than the ones you're using. I use SKS chromoplastic fenders (the ones with the P in the model number, like P50). I don't find myself ever having to readjust them.

For the front, I plan on installing one of those fenders where you attach to the downtube like prathmann is describing.

What kind of rear fenders do you guys suggest? I'm thinking of buying easy on/off clip-on types for the seatpost so that even if it gets banged up, its easy to align again.

Last year, I tried to fabricate my own abbreviated rear fender. I've also got a Topeak rear rack, which catches some of the spray. So I took a small piece of Kydex (plastic sheeting that is about 1/16" thick and can be heated up and molded) and I cut it to be about 2/25" wide and a little more than a foot long. It ran just from the chainstay bridge up to the rack, attaching at the same place where the seatpost mounts meet the rack. It wasn't beautiful, but it did catch some of the muck.

I ultimately ditched it, though. As has been pointed out, you'll still need a fender up front. So you'll probably end up with a full set. And the DIY solution isn't any less difficult to remove if you find yourself having to take the rear rack off. So why have a 3/4 length rear fender? It isn't saving any weight. It isn't any easier to install and remove. It isn't any cheaper. This was one of those projects that just didn't make any sense. I'm all for rolling your own. But sometimes it's just smarter to buy the pre-fab part that is already made to do the job. That's my two cents.

Those don't really do a whole lot. I have one. Don't use it anymore.

Planet Bike Hardcore. They are regular fenders, though. As for realigning them, just don't bang 'em up. As you said, this is your beater/rain bike. Leave it at home when you travel.

Its close to impossible to not bang it up. I have to take off two wheels, then fit the frame in my small compact car. Some part of the frame always hits my seat, sides, etc. The reason I don't want to go with regular fenders is that its always the most exposed fragile part when I'm trying to put the frame in my car. With the clip-on's, I'm hoping that even if it does get banged up, I can get it aligned quickly and go on my way.

My goal is to use this bike on rainy days for my weekly climb instead of exposing my "good" bike to the elements unnecessarily...

Same situation on my winter beater bike. So run some plastic, coroplast or vinyl siding on the bottom of the rack, sticking out some from the end. On the back side of the seat post, run some more plastic, down to the chainstays, works for me, pretty good coverage.