I have a 2004 Spectra bought it new and I use Mobil 1 synthetic 10w30.  You
don't have to use what I use any 10w30 motor oil will do.  As for
transmission fluid I'm going to give you what the manual says since I
haven't had to change/add the transmission fluid myself.  The dealer did
that for me earlier this year when I brought my Spectra in for it's 30k
scheduled service.
The following is from pages 7-47 and 7-48 Kia Spectra's 2002 owners manual

Page 7-47
Lubricant                                    Classification
Engine Oil *1     API Service SG or SH Energy Conserving-II
                        (EC-II)(SAE 10W30, 7.5W30)

Manual transaxle oil        API Service GL-4 or GL-5 (SAE 75W90)

Automatic transaxle fluid*2        SK ATF SP-III or Diamond ATF SP-III

Power steering fluid        PSF-III

Brake/clutch fluid        SAEJ1703 or FMVSS116 DOT-3 or DOT-4

*1 Refer to the recommended SAE viscosity numbers on the next page.
*2 Only SP-III classification automatic transaxle fluid should be used.
Do not use DexronIII, MerconIII, MerconV ATF or Type 7176 Fluids.
The use of non specified fluid could result in transaxle malfunction and
failure.
See your Kia dealer for the correct SP-III automatic transaxle fluid.

page 7-48
The word wrap won't allow me to actually type out the chart so I'm going to
simplify it.
Temperature Range for SAE Viscosity Numbers
5W30 Celsius -30 and below to 0
          Fahrenheit -20 and below to 40
30 Celsius 0 to 45
    Fahrenheit 40 to 120
5W20 Celsius -30 and below to -20
          Fahrenheit -20 and below to 0
20W20 Celsius -10 to 20
            Fahrenheit 20 to 80
40 Celsius 30 to 40+
    Fahrenheit 100 to 120+
10W30 Celsius -20 to 30
            Fahrenheit 0 to 100
Now the following part of the chart combines 10W40 with 10W50 and 20W40 with
20W50.
Celsius -20 10W40  30 10W50  50+
Fahrenheit 0  10W40  90 10W50 120+

Celsius -10  20W40  30  20W50 50+
Fahrenheit 2-  20W50  100  20W50  120+

Hope this helps.

Sal