I have been through a few DACs. Different chip types do have a certain sound character, but the same chip type can sound completely different, depending on the implementation and output stage (I may not be using the correct technical terms, I am not an engineer).
I will say that if I were to rank the different chip types I've heard, it would look like this in terms of descending sound quality.
FPGA
AKM
R2R
ESS
If you're going to limit yourself to a "starter" DAC (a budget might be more helpful to qualify what that means to you), then you're going to get different sounding starting DACs. They will have less drive, dynamics, detail, and musicality than the better DACs.
The MHDT Orchid is a good recommendation in what I would consider entry level. It has a nice "analog" like sound that is very easy to listen to. It's an R2R DAC with a tube. You can roll the tube, as well as the chip to change the sound and there are other ways to modify it if you're so inclined. Customer support is top notch as well.
I like the sound of the DAC in my TEAC NT-501 streamer/DAC, but there have been reliability issues with the network cards. If you're using USB input, that would be a good option and you could probably find a reasonably priced used one. I would not recommend one if you want to use an ethernet connection. It has more drive and detail than the Orchid.
I think you're better off saving up for a higher end DAC, which in my case ended up being a Rockna Wavedream Signature DAC, which is FPGA based. It was a significant improvement in sound quality over the Aqua La Voce S3 FPGA DAC I previously owned, which in turn was better than the Orchid or the TEAC.
When you get to the level of the Rockna or similar DACs, I think you're in the "sweet spot", where your extra investment provides a significant and easily noticeable improvement in sound quality, while when spending more you start to get into the land of diminishing returns and/or audio jewelry.
