You can use the microarray chip is fast and allows you to genotype 300 SNPs at a time

Since u have mentioned that ur interested in genotyping 300 specific SNPs, i would suggest that you go for SEQUENOM or SNaPshot assay. This methods are more cost effective compared to micro array. 

If you need very accurate results you won't get  around sequencing (as microarrays etc. work with light intensity, which is always less accurate than single light pulses). This can take a lot of work and be quite expensive, depending on the sequencing method you choose. Sanger sequencing is not really viable, as you would have to create a multitude of primers and run literally thousands of PCR reactions. Next generation sequencing would be preferable, as you can cover far more ground that way, but it depends entirely on the machines at your disposal.

My choice will be Sanger sequencing because I find it more accurate than other methods when I need to confirm a variant, but as Patrick Marcinek said, it can take a lot of work and be quite expensive. I agree with Patrick Marcinek as well in that Next Generation Sequencing can cover far more ground but variants should be confirmed by Sanger sequencing as it is till the gold standard if the analysis needs to be accurate.

Sequenom MassArray

The method of SNP genotyping will depend on what instruments you have available in the lab. You mentioned you have 300 specific SNPs that you would like to genotype and you have 600 samples, in this case I would look into custom genotyping arrays. For example Illumina offers a broad range of custom genotyping array options for flexible design of 48 to 1M variants (in your case it would be SNPs). Another way would be Taqman SNP genotyping, however the number of SNPs you can detect in one run is much more limited here (dependent on a instrument used, for example LightCycler 96 by Roche allows 4 variants to be detected in one run).

You can use illumina iScan, custom SNPs.

I agree with some answers before. I would use custom microarrays. It seems to be the fastes and relatively cheap way to go. Good luck!

It depends on your budget really, and what equipment you have access to assuming you only want to design the assays and not buy a platform. Only 600 samples takes microarrays off the table I think. Sequenom is probably better at this range. Please keep in mind that regardless of your choice of platform, it is not likely that all 300 SNPs will convert (work at all), and those that do convert will not all work with the same accuracy nor will they always produce a genotype in every sample (call rate). The only way you get really robust arrays or multiplex SNP assays is to iteratively design them - make a design, test, remove SNPs with poor accuracy, poor repeatability, or low call rates, replace with other candidates, repeat, until over 99% of the SNPs are giving over 99% accuracy in over 99% of sample, but you (or your budget) decide when things are "good enough". Thus, if you know of "perfect markers" for your SNPs of interest - anything in perfect LD (use r^2 not D') with the SNPs you are interested in, you might want to line those up as additional candidates to replace any of the 300 SNPs you can either not genotype because they fail the platform's chemistry requirements, score low on the manufacturer's assay design tool (e.g., Illumina's ADT or equivalent), or empirically fail tests. 

Sanger sequencing has the advantage of redesigning PCR primers, sequencing primers, and re-running failed samples on a per SNP basis, as opposed to designing a 300 SNPs at once multiplex assay. Oligosynthesis is where everything becomes expensive, and why many assays start to get very cheap *per sample* once you plan to do >1000 samples. Ordering PCR primers is the same - you can get a lot more for very little additional cost over the lowest cost option.

I'd suggest the Fluidigm nanofluidics platform. We use this for non-invasively collected samples with high success (and v low error rates). 

http://onlinelibrary.wiley.com/doi/10.1111/1755-0998.12307/abstract

This works in a 96 SNP x 96 sample format... Also very fast, and replication is cheap once you have had the assay designed and synthesized.

If your 300 SNPs are focused on specific genes, there may be a tool that has a majority of these snps already on it for an off the shelf price and turnaround.  I am seeing arrays for human studies moving to disease specific (eg Psychiatric Disorders array in form of PsychChip, Onco predisposition array in form of OncoChip) and ethnicity-coverage specific (eg, Human ZhongHua for Chinese populations supplemental coverage, African Diaspora Power Chip for supplemental coverage on African populations).  It might be useful to run your rsIDs through the ADT and/or NCBI dbSNP and just get a readout of the tools where these SNPs might already be captured.  As Mark says, it is quite likely you will be looking at a percentage of the snps that you want as a tradeoff for turnaround time and price per sample.  BTW, the mean and median phred score for the majority of reads on a MiSeq or HiSeq exceeds that of Sanger Sequencing so accuracy on NGS really comes down to a tradeoff in coverage for price.  Groups are now able to do 100-200 SNPs multiplexed in a single lane for sub $10 per sample.  These are targeted PCR based (not unlike Fluidigm) mutiplex methods being optimized for parentage panels in Agriculture.  

The Sequenom MassARRAY platform is the best in your situation!