85 Corolla Strange Symptoms

[Fitchman]

I'm not certain if this is a fuel pump/fuel filter issue, or a electrical/starter issue.
Here's the history...

I have a 45 mile one way commute daily...

I've had problems with my Corolla hesitating when the engine is cold, like at a stop light. When trying to go into 2nd gear it runs rough, and has stalled. I mentioned the engine being cold, because I didn't have this problem when leaving work.

Once or twice at highway speed, I've had a serious hesitation, like it was going to stall... fuel filter right? This only happened once or twice. I figured bad gas...

More recently, the car wouldn't start at all. I went to start it, and it turned over three times, then just a click. That's it. I figured.. bad starter.

Three days later, I went to test it again, and it started up with no problems.

Perhaps I have multiple problems... the starter may be going out?
The fuel filter probably need replacing...? I don't know where the fuel filter is. I'm sure it's outside the fuel tank...

[Fitchman]

I replaced the fuel filter this morning. I'd been about a year. The car is taking a while to engage. I wonder if the choke needs adjusting. I've determined the starter is fine. Every time, except one, the engine has cranked over just fine, just slow to engage...