Budget to get yourself a Roku because even die-hard TiVo lovers admit the on-line experience via TiVo is LESS than desired. I also say that from personal experience. As someone who subscribes to all the major on-line services, for evaluation purposes for possible cord cutting of some kind, and also have several TiVo's for OTA to take pressure off my Hoppers.
First, Amazon Prime is NOT available on the Premiere, but is soon to arrive to Premieres and Roamios, but ONLY in STREAMING service, no downloads to the HDD. What you have on the Premiere now is Amazon Instant Video and while you can download that content to your TiVo, all the content is either RENTED or PURCHASED for a cost, no free content included with your Prime account. Further, as much as I love the Prime service for its 2 day delivery and access to the LIMITED free content that I can stream or load onto my Kindle Fire HDX for viewing without an internet connection (although Amazon does impose some SILLY limitations) it is really the poorest value for free included with the Prime service. Much of what people want to watch is PAID content beyond the Prime. Amazon does seem to have overall better PQ along with Hulu Plus while Netflix is abominable PQ and audio Q far too often.
As much as I despise their PQ and audio and lack of content I would watch, Netflix is really the best value by far for everything at ONE price. No navigating the paid stuff and free included content of Amazon's dopey model, and you will rack up a lot of if you buy content from Amazon because it is EXPENSIVE. But Netflix has a great library of OLD CRAP we have all seen before.
Hulu Plus, has by far the most never seen in US (original and new to us) content and with often great PQ and audio. No the same content is NOT available across the big 3 streamers. But, then again, Hulu doesn't have as many movies as Amazon (most of which are NOT included with Prime,and the TV shows are sometimes FREE for the first season and PAID for subsequent seasons) nor the breadth of OLD TV shows Netflix does, but Hulu Plus fills a needed desire (FRESH programming) important to me.
I was really excited about these services when I signed up for them, but I have found far more frustrations and limitations and disappointment than I anticipated. Just a few include that the most RECENT episodes of current shows just are NOT available for over a year, often 2 from original air. Also, the streamers LOSE rights to a media company's content like Dish may lose channels, but with streamers, this loss is FOREVER to years. So, that show you had been watching or were counting on being available to watch when ever you want, is no longer available. So much for the cloud on that! Oh, that show that Netflix no longer offers is on Amazon (possibly at a cost beyond Prime) or Hulu Plus, but now you INCREASE your COSTS by having to subscribe to more than one, often ALL 3 of them.
Perhaps better, especially if one want to really save money, is, as I mentioned, getting the Roku not only because it is the BEST and most reliable streamer around with the BEST remote with that "Skip Back" button (and you can NOT skip back on the TiVo's with streaming) but also because Roku has a ton of "junk" channels that are free or advertiser supported such as independent or art films only channels, really old-time TV shows like the old Betty White show from the 50's, and UFO channels, and horror film channels, etc. So, if you can fill your TV watching time with that and live without a lot of fresh content from OTHER than OTA, then it can be a good alternative.
As mentioned, CBS is now offering it O&O stations streaming (just like watching live TV at home) along with ALL its current network TV content and a library of old CBS shows like the original Dallas all for one low monthly fee. In other words, one can now watch the entire CBS network line-up, and local news for one low monthly charge. Of course, this is the beginning of the end of FREE OTA TV, as the kiddies and cord-cutters have been waiting for something like this for a long time. You should enjoy it while it lasts, probably another 5 years tops.
What is happening is the often desired "a la carte" channel option that is truly the nightmare: a fee for CBS, a fee for NBC, a BIG, BIG fee for ESPN, HBO with its coming new on-line service at who knows what priceetc. and etc. and these are all entities with greatly desired content, not junk. Those media companies are moving away from giving Netflix the content for so low a price. Netflix has already announced it is raising prices, Amazon already has, and nowhere to go but up and up and add the internet service and the datacaps and what is happening is that the LOCATION of the content is changing, but the prices are well on their way to being what people today consider outrageous for Pay-TV, or already as high or higher than a cable or sat bill because of all the on-line services, ONE level of service to all from the cable cos which cost a minimum of $50 a month (the Comcast model being adopted by Charter and more in growing areas) but, the ISP's say, you are getting 50Mbps (or in some cases 100Mbps) for all that money, and what you have is the SAME costly monster, but in the costume of being accessed with a technology with which the young-lings are most comfortable and cord cutters never get the see the total cost of the changeover on a single bill, just lots of little charges for each piece of the entertainment pie. Now add to that the coming NuTV from Dish and other coming "low price pay TV via internet streaming" that cord cutters have been begging for from companies like Apple, Amazon, etc. (often the $30 price point has been cited by several as what they would be willing to pay such a service that can bring them ESPN and few other channels they greatly miss) and one can go over what they are paying for pay TV today.
BTW, if you are handy, great. But if you are not, get ready to pay Weaknees tons of $$ to repair your Premiere. I really would have recommeded the Roamio for you because it has 4 tuners, is compatible with the Mini and anyone can change-out the guaranteed to fail HDD with NO special tech knowledge. Just open it, take out the old HDD, and connect and install the new HDD, and then plug in the Roamio and it all takes care of itself and you are good to go in minutes, unlike previous versions of TiVo that require you to mess and load the appropriate software--careful it is the correct versions for your generation of TiVo--as a totally inefficient method of changing out HDD's . And yes, the Series 3 does have a better OTA tuner, and so does the Roamio. The Premeire is NOTORIOUS for its frustratingly lousy OTA receptions except in the most ideal of conditions.
My point is they have us coming and going. We're never going to escape the greed of the big media content owners, but a few years of being ahead of them provides a touch of satisfaction, for now.
Well, to each his own. I do wish that I had viewing taste to do a cord cutting event, but I have been doing it somewhat for almost 2 years now, and it isn't even CLOSE to getting me to cancel pay-TV, not for what we watch.
FWIW, I have been watching Star Wars: Rebels on DisneyXD on-line, but one MUST have a subscription to the channel via a pay TV service (and that is all too common, so I will miss out on MORE content by cutting pay TV) because it is in HD while Dish is LATE in providing XD in HD.
Good luck though and enjoy the extra $$ for as long as it lasts.