Assuming that the clutch is fully releasing when you press the clutch pedal, the roughness you feel moving into first or second gear indicates the synchromesh for those gears has worn.
Shifting requires that adjacent gears in the gearbox mesh together; this meshing is challenging because the gears rotate at different speeds. Synchromesh is a mechanical assembly between the two gears; using a metal ring between the gears, the two gears are brought to the same speed. When they're at the same speed, the gears can mesh smoothly. Each gear pair has synchromesh. You can read a bit more about synchromesh in Wikipedia.
Synchromesh rings are the parts that change the gears' rotation speeds by making metal-to-metal contact with the gear faces; the rings are under the greatest stress in first gear, and are most likely to wear. In higher gears, the strain on the synchromesh is less. Thus, wear is more common in the lower gears, and appears earlier.
When shifting into first, try shifting into second or third before you move the shift lever into first, to take advantage of those gears' healthier synchromesh. You don't have to release the clutch pedal; just press the clutch in, shift into second or third, move the shift lever to first, and release the clutch to drive away. The engagement into first (after being in another higher gear) should be smoother. Don't force the gearshift, shift in a leisurely fashion. When first starting out, you may find things go easier if you push the clutch pedal in, wait a few seconds, then begin to move the shift lever.
Make sure the gearbox contains the correct quantity of the correct oil. If you change the gearbox oil, make sure there's no metal bits on the drain plug. If there is, it's likely time for a rebuild.
Other than the right quantity of the right oil and a correctly operating clutch, there's nothing else to be done from the outside. Replacement of the synchromesh rings will require removal and rebuiding or replacement of the transmission.
