First, there are plenty of boats that would suit your needs that will not cost the full $25,000 you're budgeting. I also recommend that you reserve at least 15-20% of any boat buying budget for refitting, upgrading or otherwise modifying any boat you do buy.
First, on the size of the boat—just remember that the costs of ownership and maintenance go up with the size of the boat. Each additional 10' of boat tends to double your costs... a 25' boat will cost half of what a 35' boat does in maintenance, dock/marina fees, etc. While this isn't a perfect rule, it is good enough to use as a guideline.
Second, a 30' boat is not 20% larger than a 25' boat. It is more like 70% larger than the 25' boat, because boats grow in three dimensions, not just length, but also depth and width. While there are exceptions to this based on the design, this is a good rule of thumb.
Third, IMHO, standing headroom is not half as important as having a good berth that you can stretch out in and sleep comfortably in. Most of the time when you're down below on a sailboat, you're sitting down. If you need to stand up, that is what the deck is for.
One question for you is how important is sailing the boat to you? The boats that will make better liveaboards will often have less than stellar sailing characteristics, since the features a good liveaboard often requires are often not conducive to good sailing performance. High freeboard, excessive beam, open interior layout, etc... are generally not great characteristics for a smaller sailboat.
I would also recommend that you go slightly smaller and go for a higher quality boat in better condition than go for a larger boat in poorer condition. Starting with a boat in poorer condition means that you may have to sink more money into the boat to maintain and upgrade it. Be aware that some marinas have a minimum LOA that they will require for a boat to be used as a liveaboard.