Do you have a tach? Sounds like you are just bogging it or not rev matching right if it's jerking and rocking. In a small engined car the momentum of the drive train and mass off the car easily overpowers the engine and can cause the car to buck, rock, bog, feel no power at all with your foot to the floor to where it feels like slipping, etc, if you don't shift at the right time or allow the RPM the drop too low. That feedback is normal being that there is no play or slip in the drive train like there is with an automatic's torque converter. If you are in the wrong gear or too low RPM for your speed and the wheels aren't tuning, the engine and drive train are going to bind up and cause bucking, shuddering, etc, and if you are in too high a gear, trying to accelerate will have zero effect (perceived as slipping?), especially if its not a torque-y engine down low.
How high do you rev before you shift and whats the lowest you get when you are driving? With a 4 cyl, cruising should be 1,500-2,500 RPM and never lower unless stopped and idle. Don't be afraid to let it go up there and scream if you need to get moving in a hurry. If you had an automatic and it had a tach, you'd see the manufacturer allowing it it go to 6,000+ (or a few 100 RPM from the red) every time before the first shift. That first shift from first to second is the biggest change in gear ratio and would cause what you describe if you shift to early in first without enough revs.
The lower gears are also really low and the car is going to be really sensitive to the slightest creeps in the pedal below your right foot, and once you get rocking, your foot bounces and the problem just compounds until you let off and wait for it to smooth out again.
If it's you, don't worry about it, you'll get used to it and get better. Every car is different anyway and no matter how good you car, you can easily drive like a n00b in a different car right off the bat. I have a terrible time switching between driving a Camry 5 spd and a Cobra 6 spd when I haven't driven one or the other in more than a week. It's especially entertaining slamming the Camry's clutch pedal into the floor like a feat of Hercules...
To know if it's the clutch, accelerate to 25-30 in 2nd, then shift into 5th, let off the clutch completely and, and floor it. Does the engine scream and the acceleration of the car doesn't feel proportional to the rising RPM, almost like neutral? Then the clutch is slipping. Otherwise you will see the engine RPM drop immediately and the car will have no power at all. Then the clutch is working properly. You can also slowly and gently climb the revs high in second, let off and coast abruptly, then rapidly accelerate again and that would slip the clutch also if its not holding well. The engine will rev extremely quickly or sound weird going up and down as the clutch struggles to take hold.
Stock OEM clutches aren't all that super expensive, maybe like $150 for a clutch set. Not sure about labor. It's a easy do it yourself job if you know what you are doing, but if it's front wheel drive transverse mount, it's easy to get overwhelmed and you are also dealing with suspension/brake/axle components which could be a safety issue if you don't know what you are doing putting it all back together. The clutch itself is a 5 minute job, but on a FWD car it takes like an hour to get to it!
Could also be pedal position or linkage adjustment that is out of whack.
No offense but I think it's just you personally, because I do the same thing in my Camry if I haven't been driving it in a while until I re-adjust, usually in like a day. And every car I have ever owned has been manual.
Wow, and I'm extremely chatty tonight... boring rainy Friday night.