An error of 200 s.f. or more on a 7000 s.f. lot is unlikely. +/- 50 s.f. would not be uncommon. Also, any amount of discrepancy that exists, whether or not significant, is just as likely to show the lot being less than 7000 s.f. as it is to show it being more.
There are 5 different statutory triggers that if encountered by the surveyor, would require that a record of survey be filed. Dave K mentioned one of them. If none of the triggers are found to exist, the surveyor may still file the record of survey if he believes one should be filed, or if you direct him to prepare and file one.
Preparation of the map, assuming simple to moderate complexity in your survey would typically add between $300 and $800 over performing the field survey without a follwing up with a map. The county that you live in can make a big difference in the amount of review fees you would need to pay. Orange County is free. I've heard that San Bernardino can run 4 figures on even relatively simple maps (Peter, Ryan, or a couple others may be able to clarify that based on direct experience). I think that LA County charges $100 or $200 - fairly nominal compared to many counties.
As long as you contract with your surveyor to show the buildings and ensure that he will also show fences (many don't even when they should, unless specifically asked to do so) on the record of survey, you won't be gaining much by contracting for an ALTA. An ALTA has a specific certification that cannot be placed on a record of survey and has other formatting differences from a record of survey. If, while performing the survey for an ALTA, one or more of the statutory triggers for requiring a record of survey are encountered, you will be paying for the survey, the record of survey map & any associated county review and recording fees, the ALTA map, and quite possibly some premium if the surveyor factors in any for perceived additional potential liability associated with the ALTA (has to do with the certification and the various parties that may be included as being certified to). Unless your lender is requiring the ALTA, save the money by just ensuring, and contracting for the surveyor to show the improvements that would be shown on a basic (no Table A items) ALTA. Be specific but don't get carried away. Showing fences and basic outlines of primary buildings on the record of survey is reasonable. Showing all sidewalks, utility features, swingsets, all patio and pool features, etc. will quickly make the record of survey too cluttered.
Having a survey performed in connection with a real estate transaction is not a legal requirement, but neither is having a mechanic's inspection before buying a used car. Both, however are highly recommended and the wise buyer would do each for very similar reasons. Negotiate a credit on the price of the home to cover the cost, or at least part of the cost of a survey.