I agree with Primer3 plus software being great, but strongly recommend you to use NCBI's improved version called 'Primer BLAST'. The key advantage is that it will BLAST your primers against the reference genome, so you make sure that they are specific to the amplicon you want to get.
If by any chance you wanted to read some background info on primer design, I published a short article on the subject where I explain the basics.
Primer3. I don't change any parameters. Just paste in my DNA sequence, select amplicon size and go. If it's for RTPCR and I want primers in different exons, it's easy to mark on the sequence the position of the exon intron boundary to request primers on different exons.
When I was designing my primers, I found that CLC Main WorkBench was a perfect tool to design primers and assess primer parameters, due to its easiness of handling and a good visual interface for users. The bad part is that it isn't a free-software, so you'll have it in a free mode for 1 month, and after that, you can use the basic tools (not include Primer Design), but if you can buy a license, it would be perfect!
We use SE-Central. Although you mostly download your sequence in that and you can design your own primers. You can also do some cool in-silico analysis like plasmid construction, restriction enzyme digest analysis, molecular cloning etc.
I agree with Primer3 plus software being great, but strongly recommend you to use NCBI's improved version called 'Primer BLAST'. The key advantage is that it will BLAST your primers against the reference genome, so you make sure that they are specific to the amplicon you want to get.
If by any chance you wanted to read some background info on primer design, I published a short article on the subject where I explain the basics.
I very much agree with Ruben Alvarez-Fernandez' comment. I have designed many primers with that strategy. It is necessary to check how many products a primer pair can amplify. If more than one (with adequate sizes), then it shouldn't be used.
I recommend the OLIGO5 or 7 software. They present all the essential choices. Of course it is necessary to check the primers (designed using any software) in the target genome using Primer-BLAST which provide by NCBI. This step helps to avoid false priming.
I also recommend Primer Blast because you can use it to check if undesired products from possible contamination could cross-react with your desired target, in case of cultures.