We present observations and initial analysis from an HST/STIS program to obtain the first co-spatial, UV-optical spectra of ten Galactic planetary nebulae (PNe). Our primary objective was to measure the critical emission lines of carbon and nitrogen with unprecedented S/N and spatial resolution over UV-optical range, with the ultimate goal of quantifying the production of these elements in low- and intermediate-mass stars. Our sample was selected from PNe with a near-solar metallicity, but spanning a broad range in N/O. This study, the first of a series, concentrates on the observations and emission-line measurements obtained by integrating along the entire spatial extent of the slit. We derived ionic and total elemental abundances for the seven PNe with the strongest UV line detections (IC~2165, IC~3568, NGC~2440, NGC~3242, NGC~5315, NGC~5882, and NGC~7662). We compare these new results with other recent studies of the nebulae, and discuss the relative merits of deriving the total elemental abundances of C, N, and O using ionization correction factors (ICFs) versus summed abundances. For the seven PNe with the best UV line detections, we conclude that summed abundances from direct diagnostics of ions with measurable UV lines gives the most accurate values for the total elemental abundances of C and N. In some cases where significant discrepancies exist between our abundances and those from other studies, we show that the differences can often be attributed to their use of fluxes that are not co-spatial. Finally, we examined C/O and N/O versus O/H and He/H in well-observed Galactic, LMC, and SMC PNe, and found that highly accurate abundances are essential for properly inferring elemental yields from their progenitor stars.
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